You can use the word "collect" to talk about getting money or items from people for things like:
- a charity
- buying someone a gift together as a group
The phrase "take up" is also used in a similar way:
Excuse me, we're taking up donations for the Haiti Relief Fund. Do you have a moment?
However, "take up" only works with money. You can't "take up" canned goods. "Collect" works with both money and physical items.