Consider: to think carefully. I usually use this word when I am choosing between options so I am 'considering' my options.
Presume: this word is not very common and most people use it interchangeably with assume. The difference is that presume is usually based on a little evidence or circumstance, but assume is usually not backed up by anything.
Assume: to decide that something is probably true, with little evidence. Example: I assumed that my friend was mad at me because she didn't answer my call.
Suppose: suppose is usually used when considering, or thinking about, future options. Example: Suppose I lied to my Mum. Do you think she would be mad?
Some people also use this when settling for a decision. Example: I suppose that would be alright.
Hope this helps!