The public transport system in Budapest is superb, and the traffic terrible, so it's a no-brainer. The new trams are the Bentley turbos of trams. Get a carnet of ten tickets at any metro station, and they are good for all transport. You must validate a ticket for each journey or part of the journey if changing. There is a brilliant website (transport maps do not exist) with an English version. This gives all routes, maps, intersections, stops - a really informative and useful site:
www.bkv.hu/angol/home/index.html
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The book of 10 (or 20) tickets is useful if you're doing the occasional trip during your stay, but consider a tourist pass if you'll be hopping on & off.
The metro is a confusing state of affairs. You need to validate a new ticket if you change metro lines - a not uncommon occurence. Fail to do so, and you will probably encounter the heartless, stasi-trained ticket inspectors at some stage, who will cheerfully fine you (without fail) the equivalent of a tourist pass.
Look out for orange, shoe-box-sized boxes to validate your ticket. English is becoming more prevalent on the transport here, but don't count on it.