Munich Airport is about 30-40 minute train ride from the city centre. Taking a taxi would be really expensive all the way to the centre of the city, but hey that is up to you! It would take about an hour I guess.
Along the exit you will come along the train ticket machines. The tickets will include the train, tram, buses and uban you need to take - it include all of them. Just be careful you choose the correct ticket. From the airport to the main city it is the XXL ticket. Which is 10Euro for a single person or 18euro for the same ticket for up to 5 adults. So in theory you could share this ticket with a few freinds or even strangers. Note 2 children under 12yrs are considered 1 adult.
Once you have bought the ticket you must stamp it with the date to make it valid. It is valid till 6am the next day. You can keep using it all around the city or even back to the airport if you were going back again.
A tip here - locals arriving to the airport will often want to sell you their ticket they bought to get to the airport. The ticket is indeed still valid (till 6am the next day) so go ahead and buy this if you get a chance. For a single ride you would pay 5Euro and for the multi person you can pay 10 Euro. Then everyone's ticket is cheaper!!! BIG NOTE - careful to be seen doing this by the German police as technically this is not allowed. However all the locals do it anyway. So don't be confused when people ask you this - just check the date on the ticket and all is good!
Once in the centre there are then tram or Uban(metro) connections to the rest of the city. You will need to do some research first though as the stations they stop at are not listed on the screens above. You will need to know the number of the Uban/tram plus the las destination for the direction you need to go. Then you will be on the right track. Otherwise you could end up going somewhere totally different! I know I nearly did that a few times.
To understand the direction you need to go, there are sheets on the walls with the map and all the stops of the tram/uban lines. Munich is pretty big city so give yourself a lot of time.
Taxi's within the city are not expensive considering they are in Europe. However I think this is because mostly they don't try to cheat you and there is not too much traffic in the city so the rides go pretty smoothly!
Anyway Ciao for now!