piece together	learn the truth about sth by considering all the separate bits of information you have
puzzle out	solve a confusing or complicated problem by thinking carefully about it
read up (on/about)	get information on a particular subject by reading a lot about it
swot up (on)	study something very hard, especially for an examination
take in	1/3) understand and remember sth that you hear or read 2/3) accept sth as real or true
take in	3/3) trick someone into believing something that is not true
think over	consider a problem or decision carefully
think through	consider the facts about sth in an organised and thorough way
think up	invent or imagine something, especially an excuse