Rats are very clean animals, and usually do not require bathing. However, it is a good idea to do so every once in a while, or of course if they get very dirty.
One of the easiest ways to do so is to use your bathroom or kitchen sink. Fill the sink with an inch or two of warm water, and have your shampoo and a towel ready. Only use no-tear shampoo (baby shampoo or pet shampoo usually are) just in case you get any in your rat's eyes. Bring your rat into the bathroom and gently place him in the water. Most rats do not like being wet, and he will most likely try to climb up your arms. Gently hold him and get him wet all over, then drop a tiny bit of shampoo into his fur and work it in. I usually don't even bother shampooing the head, rats really dislike it and it is hard to keep it out of their eyes when they squirm. Once he's lathered up, rinse him thoroughly using either the water you had in the sink or run the tap over him, if he'll let you. Often rats defecate during a bath, so be ready.
When he is rinsed off, wrap him in the towel and dry him off as thoroughly as you can. You can use a hair dryer if you wish, but only on the lowest speed and heat setting. Usually this just scares the rats, a towel is most often enough. After he is fairly dry, he will begin to groom himself all over. You can put him back in his cage at this point, just make sure that he doesn't get cold.
As an alternative to bathing, you can wet a soft washcloth or gauze and give your rat a quick rub-down. Baby wipes (non scented) are also good for quick washings. It won't be as thorough or a clean as a bath, but it's nice if you want to freshen them up quickly.
Trimming Your Rat's Nails
Some rats are active enough that they do not need their nails trimmed very often, if at all. For the lazier ones, however, you will probably find that if you don't trim their nails, they can scratch you when you take them out to play, and though small, their sharp little nails still can hurt and irritate your skin. There are a few things you can do to help your rats wear their own nails down inside their cage. Some of those ideas include putting a rough brick in their cage in a place where they have to cross over it, filing their nails down in the process. I've heard some people claim they put sandpaper in their rat's wheel, but I wouldn't recommend this, as sandpaper can't be very good on the soles of their feet, which would touch the wheel more often than their nails.
To manually clip their nails, I find it best to use a baby human nail clipper, not one made for dog and cat nails, as those are often too large. If your rat is very good with being held, you can often just take your rat onto your lap, hold his body with one hand, gently pinching each foot between your thumb and index finger with your left hand and clipping his nails with your right. You should take your time while doing this, as if you rush you may cut too far and cause him to bleed.
Sometimes it is easier to do this while your rat is in his cage. Entice him to climb up the side of the bars with a treat or with praise, and as his toes grab the bars, they will be hanging on the outside of the cage where you can easily trim his nails without him moving too much.
If your rat is really wiggly, or you are afraid to trim his nails, try a nail file or emery board instead. This can polish down the nails to a smooth tip rather than taking a big chunk off at once. There's no way you can hurt your rat using this method, though it may take a little longer than using a nail clipper.
Rat nails grow very quickly, and if you like them to be dull and short, you will have to trim them once or twice a week.