Hi,
The train is about 35-45 mins from the centre, you can get the S8 or the S1 train from there - the trains terminate at the airport and the station is directly in/under terminal 1 so you can't really go wrong. Follow the signs with a green circle with a white S in it. Check where you are staying as the S8 goes one way round the city and the S1 the other way, although they both end up in the centre in the end.
the Allianzarena is about 20 minutes from the town centre on the U6 - you get off at Frottmanning. This was my journey to work for 3 years (well a few stops more to Garching) so I know it well, was amazing to see the ground going from a field to what it is now! The ground is so much nicer than the old one in the Olympiastadium where you could be miles from the pitch.