Czech republic is a small country, less than 500 km from end to end. That can be covered by bike in a week without excessive effort, so you don't need to spend your whole annual leave for one little trip. I have several such trips under my belt and the gathered experience might be of use for others, so here it is:
One of the possibilities is to find a hostel or dormitory and spend the night with all the comfort of civilization. But you need to find some which is open, has available room and provides safe parking for your bike, and all of that right at the place where you end up that evening. Too many conditions for my taste.
Another possibility is to camp in the wild. Forests are usually no more than 10 km far and you can see by a map if there's a ridable trail in them. One of my reasons for choosing forests is that my tarp needs two trees for support (a self-supporting tent can be assembled on any meadow), but there are other advantages as well: more privacy, less wind and no risk of being run over by a tractor or expelled by an angry farmer. Czech forests are public, freely accessible to anyone, as long as they don't damage or pollute them.
An important rule: never make fire in forests. Summers are hot and dry, sparks fly far, dry needles and leaves on the ground can burn invisibly under surface and even if you extinguish your fireplace thoroughly, something else can catch fire long after you have departed. You can only afford fire in permanent campgrounds or during long-term camping at one place where someone is always on guard. If you can't survive without coffee or hot soup, bring a cooker.
Regarding safety, there is nothing to fear in our forests. Sometimes a deer or other animal walks by, but nothing dangerous, the only bloodthirsty beasts here are mosquitoes and ticks. Don't leave your bread on the ground unless it's packed in something sturdier than just a plastic bag, mice and dung beetles like it a lot. Ground beetles can be bribed with a breadcrumb to run away and stop rustling under your tent. Owls make various funny or scary noises, but they don't eat people. And thieves certainly don't search remote forests for sleeping rich tourists.
My daily consumption in summer weather is around 6 l. I usually carry three litres with me, refill once in the morning and once in the evening right before going to camp. Half litre is spent on washing, one litre is drunk with supper, one with breakfast and the last half is a reserve for getting to another source. It's good if at least one of your bottles is a small half-litre one, because faucets are often too low to fit anything bigger under them.
I also experimented with a filtration bottle which in theory can turn any stream into a source of drinkable water, but it didn't work very well on a bike. In the lowlands, streams may be contaminated by agricultural chemicals which might get through the filter, and clean brooks in the wilderness are hard to get to with a loaded bike. Filter is perfect for trekking on foot or for long-term camping at one place with a reliable water source at hand, but while cycling, it's easier to refill at restaurants and shops (or petrol stations if everything else fails, but some of them may not have potable water in the taps).
An evening bath needs surprisingly little: a quarter litre of water and a cloth. You get rid of stickiness and smells and flies stop swarming around you. I can't imagine doing it indefinitely, but a week is no problem - and you can surely find a shower within a week.
Rainwater is not that nice. It doesn't dissolve humans, but makes them cold and that can be pretty unhealthy sometimes. If you get wet while riding, it's best to pedal on until you get to a warm and dry place or until you dry yourself. Sitting in wet clothes under a shelter and waiting for a storm front to pass is not the best idea ever.
Nearest town or village is usually no more than ten kilometres away, so you don't need to carry supplies for a week. Just don't forget that many small shops in little villages are closed on Sundays. Larger supermarkets are usually open every day, as well as most restaurants. I like to carry ready-to-eat snacks, supper and breakfast for the whole day, and get a proper big lunch at a restaurant - that means I don't need any dishes or cooker, just a spoon and knife.
Theoretically, one could eat for free: many edible things appear in summer, just find, pick and maybe cook them. It is just a question of priorities: how much time do you have, whether you want to carry kitchenware with you, whether your conscience allows you to poach in fields (corn or potatoes don't grow in the wild) and so on.
How much a cyclist eats? A human is no perpetuum mobile, a day of pedaling does cost some energy. If you want to lose weight, long distance cycling is a perfect choice: eat only so much to not feel hungry and your body gradually adapts to burning its fat reserves. If you want to stay the same, don't be lazy and eat more than normally. My usual range between two snacks is twenty kilometres, then it's either eat or bonk (hunger, blurry vision, shaky knees and loss of power - we all know it), but everyone's limit may be different. Ketogenic diet (low carbohydrates and no sugars) is said to prevent these problems by adapting you to burn belly fat equally easily as fat from food, but I haven't tried it on myself yet.
My favourite combination for summer weather is three sets of clothes: first one for riding, second one for drying on the rack, they are swapped every day and washed when needed. Third set remains relatively clean and not sweaty and is used for sleeping and to change into before entering civilized indoor spaces. Then you need something dry and warm for cold nights (warm trousers, sweater, thick socks etc.) and some appropriate trousers and jacket for cold or rainy days.
Functional clothing works well and I can recommend it: it's light, ventilates well, doesn't feel cold when wet, and dries quickly. Wool is also excellent and doesn't smell, but it holds more water. Cotton is best for the third set only.
For winter weather, I prefer several thin layers covering the whole body uniformly, with extra bits on exposed spots. But I only do point-to-point rides from one warm house to another, so it doesn't fit the topic of this article.
Route selection depends on your priorities. If you want to just enjoy the landscape and ride for fun and sport, find a nice, safe cyclepath or trail. If you need to be at a certain point hundred kilometres away by nightfall, main roads are the best choice, but if there's a heavy traffic and no shoulder, it can be pretty dangerous. Less busy secondary roads are a good compromise: they offer both scenic views and thrilling encounters with motor vehicles, but in smaller quantities.
Caveat: there are strips of alternating light and shadow on roads lined by trees in sunny weather, which can make you completely invisible. This is no metaphor: I was once riding fifty metres behind two cyclists, looking through ordinary sunglasses exactly at the spot where they were, and when the rear one covered the front one's powerful rear blinky, I couldn't see the slightest hint of them. So be careful, it's good to shine and blink as much as you can on woodland roads during daytime. Similar problem occurs when the sun shines from behind you and there is a forest or other dark, broken background behind you. If an oncoming driver decides to overtake or turn left, they can overlook and hit you, as almost happened to me once (I keep my headlights on during daytime since then). For illustration:
Regarding means of navigation, I have tried many. A small scale cycling atlas of the whole republic fits into an A5 format book, is easy to read, handy and sturdy, but sometimes not detailed enough, especially for finding your way through a city. Hiking maps are quite detailed, but those are big unwieldy sheets of paper and you need several of them to cover the whole journey. A minimalist solution, but a surprisingly effective one, is a cue sheet where you can mark every turn and village with all the details you need and skip the boring kilometres in between. There's just one little drawback: if you divert from your planned route, you're lost.
I now use an electronic map stored in a waterproof smartphone. It is not as easy to read as the paper ones (some town names only appear at certain zoom levels), but it contains almost everything, can be zoomed from a whole country panorama down to street names and house numbers, and if you still get lost, you can get found by GPS (which I keep turned off most of the time because it is quite power-hungry and recharging from my bike's generator is not limitless). Highlighting the route with a felt-tip marker can be simulated by a GPX file created in some online map, points and labels can be added directly in the phone.
On long journeys, it's good to let your muscles work in aerobic mode, i.e. using oxygen from blood. I had a simple check for it: if I have to open my mouth for breathing, I'm working too hard. Now I have to guess, because after several months of lung training with anti-corona face mask, I don't run out of breath anymore :-). There are also more precise methods than guessing, for example measuring your heart rate or power output, but those need special instruments. If our muscles work in anaerobic mode, i.e. using their internal fuel/oxygen reserves, they produce lactic acid which makes our legs ache the next day. With a comfortable effort level (and a comfortable bike), it's normal to wake up in the morning without any ache at all. That's probably the whole "magical" recipe for long distance cycling.
Another thing which may affect leg ache is their working temperature: if they get cold, it's worse. But I can't tell for sure because my experiments keep getting thrown off by various random inputs.
How far can we ride in a single day? I was doing 90..100 km on my trike at the beginning of September. Daylight woke me up at seven and I hit the road before nine. In the evening, I headed into a forest between six and seven to prepare accommodation without hurry before darkness falls. It is certainly no racing speed, but I can keep it indefinitely, as long as I get enough sleep at night (and no digestion problems). Be sure to test your limits before you plan your holiday hour by hour, and then the last day before midnight realize you are still ninety kilometres from home, with no train available till morning and with everyone who is able to drive you home asleep and not answering your phone.
Some things are no brainer (flashlight, toilet paper, tool set), some may need trial and error to come up with:
...you suddenly realize some things. That you are in a dry, warm and windless place. That your faucet provides unlimited amount of potable water and you don't need to care how much you can drink and where to get more. That you can just flip a switch and there's light, no worries about dying batteries in your flashlight. That you can wash yourself properly. That your bed is horizontal, soft and doesn't poke you with roots or rocks. That all scary outdoor noises are blocked by a solid wall and possibly several floors. That you have a toilet you can comfortably sit on, instead of squatting among bushes, swatting mosquitoes with one hand and covering your toilet paper against rain with the other. That you have all your clothes and several days' worth of food within reach, not just what you were able to stuff in your panniers. That unexpected health problems only mean a call to work and return to bed, not being stranded in the middle of nowhere with supplies running low. That you can call for help when needed. That you won't freeze to death in winter. That living without civilization is everything but easy.