Find a car, drive it fast then apply the breaks very hard and voila! Sorry for the sarcasm. I had this connundrum a few years ago on a low budget animation. I ended up recording my brother in law skidding to a halt on a quiet country lane, a few takes was all that was needed as I then used pitching and time stretching to alter my 3 sounds to make more.

Are you needing those sounds particularly? If so then there's places like Soundsnap that are great for buying a few random sounds for very little money.

Good luck.

Ian

A hot water bottle (or anything with a rubbery surface for that matter) can be a good starting point. You can rub it on a wooden desk or something that has a very slick surface to get a screech out of it.

@wadiosound has a point when he says it'll sound cartoony. If I think about a tyre screech, not only do I hear the squealing, but there is definitely another lower pitched component, a bit more rumbly that might not only come from the tyre itself but from the structure of the car, the axel maybe, or the reflection of the road texture in the wheel-well...

If you rub your fingers over a balloon you can get some very nasty screeches, so I guess dragging a balloon over a surface with some texture could produce something similar but give you more freedom to create longer sounds.

I'm afraid anything you might try will sound a little cartoony. Depending on your production type, this may or may not work.

Your best bet is really to record it yourself. Fortunately, anyone with a daredevil mind and a car will be able to reproduced this sound.

The other option is SoundSnap (as Ian said) or SoundDogs. Both sites are great.

I hope this help.