1. He picked up the stone.

Question

2. He took up the stone.

(Are both the same?)

3. Volunteer work takes up a lot of time.

(What is the meaning of 'takes up'? What other words can we use instead of 'takes up'?

Answer 1

1 and 2 mean about the same thing, yes. 1 is the more common usage.

3 could be rephrased: Volunteer work involves a lot of time.

http://www.eslcafe.com/pv/pv-a.html
Good list of "phrasal verbs" -- look them up alphabetically.

http://www.eslcafe.com/idioms/
Good lists of idioms -- look at the whole collection or look them up alphabetically.