People here will give you different advice about the way to deal with the police. Mine is simple: be nice, but be firm, and try to assess the situation correctly.
The solitary cop
This is the worse situation, you get stopped by a policeman who is alone. There is no way of telling whether the control is official, and it’s even worse if you didn’t do anything wrong, because cops are supposed to stop you if they saw you commit an offence (except if it is a checkpoint, but that usually implies several policemen). Whatever happens will depend on your negociation skills. Don’t let yourself be too impressed, though.
Along the roads you will find some checkpoints, especially during long week-ends or holidays… or at the end of the month. The police are mostly after drugs, so you don’t need to fear anything. Lower your window if they ask you to, show them your license and they let you go.
You didn’t wear a helmet
Well, just pay the 300 baht (or something) fine and don’t go into lengthy explanations. The law requires that you should wear a helmet, period.
Pay here or pay at the police station?
When you are given a fine, they can ask you to go and pay at the police station, and leave something as a guarantee. First time I ever got stopped and fined, they wanted my wife as a guarantee but I didn’t know the area and feared I wouldn’t be able to find the police station, so eventually I left my phone! These days you are usually ask to leave your driving license at the checkpoint. So you go pay the fine, you come back to the checkpoint with the receipt and you get your license back. In some cases you can ask to pay on the spot, but you can’t demand a receipt, if you get my drift.
Speak Thai or pretend you can’t?
If you can speak Thai, I found out it’s better to speak Thai with the police rather than pretend you can’t and expect that the cop will be embarrassed and give up.