Check for signs of breathing!

If they're not breathing, then get to a vet immediately. It's not recommended for people to try this if inexperienced, but this is suggested by Debbie Ducommun of the Rat Fan Club:

"Hold your rat firmly around the neck with one hand, and by the base of the tail with the other to hold her securely. Make sure there are no objects within an arm's length. Lift the rat overhead and bring her down in a rapid arc, so that at the end of the path she's tail up and head down. This can be repeated three to four times, then give the rat a rest, check her breathing, and see if anything is visible in the mouth. This is extremely effective in dislodging objects in the throat. However, do NOT use this procedure if your rat can breathe, or you might make it worse."

If they are breathing, you can try to gently massage the back of the neck, but the best thing to do is to leave the rat to dislodge it itself. This can be difficult for you, as you might feel you need to do something, but 9/10 times they come right. Keep a close eye on him/her, and maybe separate the choking rat from others for the recovery time.

Note that the dislodging may take a few hours. People have reported that they leave it for 12 hours, and then seek medical attention, but use your discretion.

Foods that can cause choking are soft, sticky foods like syrup, peanut butter, and mashed potatoes, but others such as pizza, crisps (own personal experience!), and such can also cause it. Think before giving your rats anything, and if in doubt, ask someone in the know!