Well,
First, get a copy of Comp City by Max Rubin.
* How long does it take them to rate a player?
Ten minutes? An hour?
Longer. They rate you by average amount bet per hour for how many hours you play. An example of what the computer says about a player might be "15.5 hours at an average of $77.53/hour". They will also evaluate the games you play and your level of playing skill to determine how much they think they can expect to earn off of you per hour.
* If I'm aware that they are watching, is it a good idea
to make some bad plays?
If they suspect you of being an advantage player, you are not going to be welcome, let alone earn comps.
* How do I claim the comps?
Many ways. If you are drinking at the tables (God forbid!), your drinks are free as you play. After an hour or so at the tables, you can ask for a buffet comp. After a few hours, if you are betting high enough, you can ask the pit boss for a restaurant meal comp.
My advice is to look at a group of casinos, determine from which ones you can extract money, and select one or two that have better rooms and restaurants, but have less desirable playing conditions, and are known for loose comps. Use heavier cover at these places, and only get rated at those casinos. If, after a hard day at advantage play, you like to sit back and have drinks while you play, you might want to just be a basic strategy at your comp locations.
After a while, you will start receiving comp offers by mail. If you take them up on a mail in comp, make sure you don't "comp & stiff" unless you do not want to stay there again.
If you are staying at a comped room and playing at that location, make sure you charge all your drinks and meals to your room. You may find that the casino writes off everything, or at least heavily discounts it all.
Do not get greedy. If you receive a comp for a dinner for you and a date, do not get the most expensive bottle of wine in the house unless you have that type of comp coming. Also, tip like you are paying full price.
Talk to a host, and let them know that you would like to honestly know what type of action they expect for what kind of comp. Do not, of course, talk about skill.
Only at end of the trip,
with the receipts for room and food?
It varies, like I said, you get comps in advance (mail-in), while you are playing, and at the end.
I hope this helps.
I am sure some others will pipe in.