The downtown area as well as the quarters around it can easily be explored by foot. Many travel guides (also some english ones) contain longer guided walks, where you follow the guide book and get explanations, about buildings, churches, historic events etc. Asphalt walking can be very tiring. Wear comfi shoes and treat youself with a good coffee or small snack in one of the many bakeries or bistros. You can also just create your own walk with the help of a city map. Try to include the following spots:
Sendlinger Tor, Viktualienmarkt, Isartor, Marienplatz, Odeonsplatz, Specialty foods Käfer, Frauenkirche, Karlsplatz, . If you have more time stroll through Schwabing, Haidhausen, the Glockenbachviertel or Maxvorstadt.
Definitely take a walk up the tower you can see on the picture. It is located between marienplatz and Viktualienmarkt and you cannot miss it because it is the only one with a green roof. Going up their is one Euro. You get a fantastic overview over the city and it is good for a first orientation!
Your feet, or take your chances on the autobahn. German drivers have that high speed thing down pat. If you choose to drive make sure you can keep up or you'll have to stay in the slow lane. And guess what? People know how to merge in traffic there, unlike in this country where everyone races to be first in a traffic jam. The change is refreshing.
Once you have landed to a known place, the best alternative to get around is walk. it may take a lot, but the other choices are worse.