Paper
Look at the paper. Colored paper, especially manila and red paper, will bleed and stain the stamps. That doesn't mean you can't soak them. You just need to do so carefully, so if the paper does bleed, it doesn't ruin your other stamps. Stamps on white or light colored paper are usually fine to soak.
Cancelation Mark
Cancelation marks are designed to be permanent, and they usually are. Sometimes you will run into marks made with red or purple ink. These are more prone to run and should be treated like stamps on colored paper. You may also see nonstandard cancelation marks made with marker or pens. These too may run and should be handled separately. Most stamps will have black cancelation marks which can be soaked.
Adhesive
Self-adhesive stamps are the bane of any stamp collector. They tend to fall into one of three categories. Some will soak but take much longer than other stamps; usually several hours. A few will soak, but the soaking process damages the ink or paper, ruining the stamp. The last group includes stamps that refuse to detach from the envelope no matter how long you soak them. The majority of self-adhesive stamps made since 2008 fall in this category. Older stamps also can become unsoakable if they were attached to the envelope using glue other than that which came with the stamp.
Determining Soakability
If you're unsure whether a stamp is soakable, consider its value. If the stamp is valuable or more rare, soak it by itself and watch it carefully. That way you can remove it from the water the minute it comes off the paper or it appears that it won't come off. You also can do an Internet search to see if anyone has reported a problem soaking these stamps. Stamps that might be destroyed by the soaking process tend to be newer self-adhesive stamps, not older stamps.