1. Use public transport. It is cheap, clean and reliable. You can buy a 24 hour ticket which allows you to use all methods; trams, underground, busses and ferries. Note: the ferries only run from April to September much to my disappointment.
2. Work out what you would like to do during your visit as it may be worthwhile investing in an Oslo Pass for your stay which includes use of public transport.
3. Be prepared for the expense of food/drink but know that there are lots of free things to do in and around the city too.
4. If you’re flying to/from Rygge airport hop on the coach instead of the train. It’s cheaper, just as quick and literally takes you right to the city centre, so convenient.
5. Check out VisitOslo.com before you head off on your trip, it has lots of great info.