Where I live, we don't say paste to mean "stick", unless it's the "paste" in terms of "copy & paste" on the computer. Paste here normally refers to some type of food in paste form. So your sentence, I would say "Spread the glue on the back of your picture and stick it in your album."

In this case, they all have the same meaning. There are other situations where they aren't the same. "To glue" is to use glue to attach two things together. In particular, it almost always means we are literally using glue. There are a couple of exceptions ("Their eyes were glued to the television" doesn't mean... that), but usually this holds. "To stick" means to attach two things together. It can be done with anything sticky - I can stick a post-it note on a wall, I can stick sellotape to a piece of paper, or I can stick things together using glue. We would rarely use it to mean to attach two things using e.g. nails, screws (although it is possible). "To stick" can also be used in the informal tone to mean "to put", such as "stick this envelope into the letter box" (which means to put it in, not to glue it on). "To paste" is a fairly rare verb. It means to move from one place to another, but we usually only use it when are talking about sticking paper into a scrapbook. We also use it for computers (copy and paste, cut and paste). I might use it when talking about fixing a house (I pasted the walls). I think it's slightly more common in American English than British English.