As the other answers have already mentioned, your mode of transport of choice is the suburban train, S-Bahn, identifyable by a large white S on green background.
You will arrive at the central bus station or ZOB in central Munich which is not far away from the central station and town centre. It is located exactly beside the Hackerbrücke suburban train station. The following map (Openstreetmap predicts three minutes which may be just a tad optimistic if you’re travelling with luggage; maybe four or five minutes are more realistic) shows you the way to go:
You need to find some way to reach the first floor. In case you don’t immediately see a better option, there are stairs on the outside on the South-West; just left of the taxi symbol on the map. After ascending, cross over the small footbridge onto the street bridge, the actual Hackerbrücke. A few metres southwards and you are above the platform, ready to go back down. There is an elevator to bring you down to the platform if you can’t use the stairs.
As you can see in the map, there is only one platform. You will want to take the first train that goes to Flughafen (Airport). It can either be an S8, in which case it will arrive on the southern track, continue via central station, city centre and East station and you can board any part of the train. The other possibility is an S1 which will arrive at the northern track. If you’re taking an S1 make sure that you board the part of the train that actually says *Flughafen (Airport) and not the part that says Freising. Typically, this is the rear part of the train — but recently I have also witnessed entire S1 trains going to the airport (and likewise entire S1 trains going to Freising), typically late night or on week-ends. The S1 trains get separated in Neufahrn, two stops before the airport. (If you accidentally got on the wrong part, you can still change in Neufahrn. The part bound for Freising leaves and the part going to the airport has to wait a few additional minutes.)
Both trains run in 20 minute intervals on weekdays and are interweaved so that there is a train every 10 minutes. Trains seem to be running all through the night albeit at larger intervals. But since 7 a.m. is well into rush hour in Munich, there will be trains.
The terminus, the airport station, is conveniently located underground close to the airport terminals. There are escalators and elevators to bring you to the ground level and into the terminals. Check beforehand whether your plane departs from terminal 2 (Star Alliance flights) or terminal 1 (all other flights) and follow the signs.