It's one thing to say you should sleep in your car, but it's an entirely different thing to actually do it. Through the course of the night you'll be woken up by all sorts of noises, be it street cleaners, traffic, or a crazy homeless guy. Sleep deprivation is a common problem for the newbie wandering cheapskate but follow some of these tips and I'm sure you'll get the zeez you need to travel the next day.
Before you set out on your adventure, try taking a nap with music on or attempt to sleep in a public area. A lot of times people can't sleep in odd places because they're used to the luxury of sleeping in a nice comfy bed with no light or sound to bother them. If you can train yourself to sleep in odd places then you'll be better prepped to sleep on the road.
This is my most common method for getting to sleep when I can't. Simply close your eyes, focus on a point, regulate your breathing, and relax. It's a method that most people take for granted and it often takes a lot of practice to get right but a lot of studies have shown that it has some significant positive benefits. Not only that, but it helps you tune out the rest of the world and finally get some sleep.
Not exactly my best recommendation but if you really can't sleep then there are tons of pills out there that will knock you out cold. Birdy tends to take mild aspirin or allergy pills that have drowsiness side effects since the long term effects are less harmful and you're more likely to wake up in the morning not feeling like you got to sleep with a two by four to the head.
Eye Mask/Ear Plugs
Best. Investment. Ever. They make you look like an absolute dork, but by golly are they great to have! They really do help shut out the rest of the world and it's definitely a good idea to get a high quality set since they work better. Of course if you're going full on cheapskate, a piece of clothe for a blindfold and a good heap of cotton or tissue paper for ear plugs will do just fine.
Insomnia is a common problem when you're on the road. The noises of the night are often difficult to get used to but if you train yourself to handle it, you'll find it to be even better than your nice comfy bed at home.