Chain is an exposed part that catches most dirt and needs regular cleaning and lubrication. There are many opinions on best lubricants and cleaning methods. Some people wipe the worst gunk off with a dry cloth, drip some oil on the links and call it a day. Some simply spray the chain with WD-40 which stops squeaks and doesn't catch dirt, but washes off quickly. Automotive heavy oil is not very good because it doesn't get deep enough into the links and is very sticky. Some people lubricate the chain after washing it thoroughly. The most effective procedure is to shake the chain in a jar of petrol/gasoline which dissolves all greases and washes off almost all dirt. Petrol can be used repeatedly, dust settles at the bottom and clean fluid can be poured elsewhere. Kerosene is not that good, it takes too long to dry. Another option is water-based cleaning agents (soaps), just be sure to dry the chain quickly to prevent rusting on the inside. Chains can also be washed without removal from the bike; either with a toothbrush and a cup of cleaner, or a special washing machine:
I have tried all of the above-mentioned techniques. Regardless of which one was used, all derailleur chains lasted more or less the same, about 2000..3000 km, so I ended up with the least labour-intensive cloth and oil way. Wide singlespeed chains last longer and since they wind around two fixed points, they can't slip even when considerably elongated, so I let them work for 6000 km or more until they start to drag or make suspicious noises.
Dirt affects the chain life a lot: dust and oil together make an abrasive paste which eats chain pins quickly when it gets to them. The biggest source of dirt on your chain (and shoes and trousers) is the front wheel; full-size mudguard and mudflap work wonders. Another exposed spot is next to rear tyre, a classic chainguard helps there. Long chains of RWD recumbents are often hidden in tubes (15×1.5 mm polyamide pneumatic ones), which add some noise and resistance, but provide the second best cover right after fully sealed chaincase which can be seen on some singlespeed citybikes.
Some colleagues recommend wax instead of oil, for example a mix of paraffine, bees' wax and grease at 1/1/1 ratio [source] (reported to last extremely long regardless of weather), paraffine and bees' wax at 8/1 ratio [source] (reported extreme chain life of tens of thousands kilometres, but needs more frequent reapplication) or something similar. The paraffine lubricates and fills gaps so that there's no space left for incoming dirt. Bees' wax prevents it from flaking off. Greases and oils soften the mixture and lubricate. Apply by immersing clean chain into the molten mix for several minutes. I'm currently testing the three-component variant:
The bottom pot with water limits temperature to 100 °C, ideal working temperature is just below the boiling point. The wax mixture is thin like water in these conditions, so it gets wherever is needed. Grease didn't dissolve in it, so I used heavy oil instead (or whatever was in that bottle). The stuff looked too hard when solid, so I thinned it further with several millilitres of light oil. I bathed a new chain in it (without degreasing it first), installed it on my trike and it's been under testing since then. Previous chain (wiped and oiled every 200 km or so) elongated to 132.8 mm after 2900 km of use. The waxed chain (same brand and type) clocked first more than 1000 km (including several hours in rain) without any maintenance and without any measurable elongation. Now it has done almost 5000 km, was rewaxed twice and measures 132.7 mm. I can confirm that waxed chain doesn't squeak, rust or catch dirt, and what it does catch doesn't get inside the links. Waxing a clean chain is fairly quick and easy task, the longest part is preparation of the mixture and tuning its consistency; once it's done, you just melt and soak. On the contrary, cleaning and rewaxing of a used chain is a dirty chore involving lots of hot water, cleaning agent and black dirt; I'll probably not going to do it anymore.
If it slips, fails to shift, drags, makes crunching noises, sticks to chainrings or looks ready to fall apart, it is definitely "dead" and probably has killed all cogs as well - new chain slips on worn teeth, so you will have to replace the whole drivetrain. If you want your sprockets to last longer and stay compatible with new chains, replace old chain before it elongates too much (technically the elongation is caused by the pins wearing thinner). The threshold is somewhere around 132.8 mm, measured this way:
Or you can buy a special gauge which measures the same thing, only by sinking more or less deep between the links instead of giving you a number.
There is no law to prescribe chain maintenance (as long as a bike has both brakes, it doesn't need any chain at all), so it's up to us to choose what to do. Should we replace the chain as soon as it shows first symptoms of wear to get the best efficiency and compatibility with new components? Or use it until it falls apart and then replace completely everything? Save partially worn chains and combine them with partially worn cassette which doesn't work with new chains? And what about RWD recumbents with a triple length chain that costs more than a cassette? I saw a recommended replacement interval of 1500 km in some handbook. Racing in mud can reduce chain life to mere hundreds of kilometres. Real-world examples? A 3/32" ÈZ chain on my Favorit road bike lasted about 5500 km (but it was too much, the most frequently used sprocket got worn too), Shimano UG lasted 2000 and Shimano HG about 2500. HG lasted less than 1300 km on my Python with short and poorly aligned drivetrain, and 2700 km on my Steelmachine with small chainring, but good covering and easy angles. 1/8" ÈZ has clocked 6000 km so far on my citybike and 10000 on a folder (elongated beyond all reasonable limits, but didn't hurt the big thick sprocket too much). Shimano Nexus lasted about 3000. Anyway, chains are consumables that never last forever, so there's no point in spending too much of your life by excessive care.