What if I just use the RIT dye with cold water?

Rit, or any other all-purpose dye such as Tintex Hot Water Dye or Dylon Multi Purpose Dye, will not bond to the fiber if applied in cold water. It will just wash out miserably within a few washings. That's not dyeing, just a temporary stain. It is suitable only for a costume that will not be worn more than once or twice, not for real clothing.

If you want to use all-purpose dye, you'll have to use hot water; simmering-hot water works the best, much better than hot tap water. Get a large cooking pot, large enough for the submerged garment(s) to move freely, and simmer the clothing in the dye at 190 degrees Fahrenheit for thirty minutes or more. This will, of course, shrink many garments. Oh, and you can never again use the cooking pot for food, since most dyes are not food-safe.

If you want to keep your clothing the size it is now, you should buy some cold water dye, such as the Procion MX dye (the most popular type by far). For solid color dyeing, you will also need to buy salt (which I get at the grocery store), twenty cups or so per washing machine load, or five cups for a five-gallon bucket, and soda ash (also called sodium carbonate), which is most convenient to order with your dye.

The easiest way to dye clothing a solid color is in the washing machine, but you can also use a large bucket. See "How can I dye clothing or fabric in the washing machine?" for links to instructions.