Hitchhiking and Money
Hitchhiking usually implies that no money changes hands, no monetary transactions for the ride.
How to deal with requests for money beforehand
In Western Europe and the United States it's rare that people ask for money. It can happen though, especially in Germany, where Mitfahrgelegenheit is quite popular. As a rule guaka refuses these rides, though once he accepted a ride because it was later at night after having waited for a long time already and he didn't feel like waiting any longer.
In some countries payment for rides is quite normal, especially for locals. In Romania for example you probably want to ask if the ride is free (E gratis?). In Turkey it's rare, but it happens that drivers want money, just say "yok parra" in such a case.
What to do if a driver requests money unexpectedly
Well then seemingly the only solution is to tell them you have none! Or if you're a suck up can always fork it over.
What to do if a driver offers money
Some hitchhikers (such as guaka or quarim) refuse any offers for money from the drivers. Sometimes drivers are insisting, but if you have enough money to go by and you think it's inappropriate to receive money, you could tell them you actually have plenty of work (and income), that you mainly hitchhike for fun, social contact, and ecological reasons. Instead of money drivers very often offer you material things such as food and drinks or will give you a CD, flowers, clothes...you can decide if you want to take it or not, in some countries it is impolite not to take it.
Travelling without Money
There are some people out there who hitch hike LONG distances with no money such as the infamous Tom Thumb, who hitched from England to India with just his rucksack, a clarinet, 2 loafs of bread and GBP 0.00. There are also not so famous hitchers like Aaronishappy who hitched from Norway to Morocco, with just EUR 2 arriving in Norway and his rucksack (and coming back with NKR 20, EUR 5, CHF 4 and GBP 2, which is NKR 20, EUR 5, CHF 4 and GBP 2 more than he had when he left!).
While completely crazy it is certainly possible, but not necessarily fun. You will ask yourself several times a day "what am I going to eat" or "where am I going to sleep", you will regret ever leaving your house, but knowing that no matter how bad things get they can only get better is a certain comfort. Don't forget, though, that while you see all these fancy backpackers with their expensive train tickets and those posh tourists stuffing themselves with cakes at the hotel restaurant, they're only seeing the plastic, fake, tourist side of a country. You in your desperate efforts to survive get to see the entirety of a country, "warts and all"!
How to get stuff when hitchhiking
How do you do it then? The easiest answer is that you don't think about it and just do it. The most comfortable way of survival is to come into contact with people, which works especially well when hitchhiking. The trick here is to score food, money (if you want to accept that), a place to sleep, a map, a joint or whatever else. Often you can get things without resorting to the pity game, but if you really need to, tell them you have no money, but not so bluntly. Be "covert" about it and ask questions such as where you can eat for free, use the internet for free, or "hey, do they have homeless shelters here?" Even if they don't ask why, it will strongly smell like pennylessness. They'll usually be surprised that you really are skint and will be happy to give a hand to the weary poor traveller, usually in the form of money or food. Don't expect a treat every time you hop your jolly arse into that car, however. The trick is to be genuine in expecting nothing, because when you expect nothing, the smallest thing you get will make you happy.
When stuck somewhere, your best bet (better than just keeping on walking...) is talking to people in the street. Talk about travel related things and expand on them (i.e. directions, where to hitch, etc, use your imagination!); be friendly and genuine, and incredible things will happen. If you're travelling in a Muslim country, you can basically disregard all of this, as Muslim hospitality will clothe and feed you without you ever saying a word!
Well, as this is a wiki about hitchhiking, we don't really need to elaborate on this.
There are numerous ways of feeding yourself when penniless and travelling. Next to benefiting from people's friendliness, there's dumpster diving (or skipping, in the UK), waiting opposite of outdoor pizzerias and preying on leftover pizza slices.
As for sleeping when you're not invited back, best bring a nice thick sleeping bag and find yourself a good spot to sleep in. In cities, the best spots are industrial zones (although usually a long distance from the centre), upper class neighbourhoods, and of course train stations and airports! Train stations however will often close in the middle of the night to clear the place out of bums like you. Big stations that stay open all night such as Paris and Berlin and airports will often have security walking about to wake you up. If you're stuck in the city centre with no station or access to an industrial zone/posh neighbourhood, your best bet is to keep walking until you reach a quiet area and find a nice alleyway or empty park; but don't sleep bang on in the city centre in clear light as it increases your odds of being robbed by... a lot. You could also go to a homeless shelter, they always provide a bed and usually food. They are everywhere in London and Germany, and quite common elsewhere in the first world. Whether you're inside our outside of cities, motorway bridges provide great shelter, and so does having a tent. A tent can also be useful when you're in a city, because walking around and asking people if you can pitch your tent in their front yard is an amazing pre-stage for being invited back for dinners, showers or even beds, especially if it's rainy out.