If you leave for the airport from the Hauptbahnhof (tief) station, you will stand on a central platform between the tracks gong either direction. The S1 will be on one track going to the airport, the S8 will be on the other track going the other direction. Take whichever S-Bahn to the airport comes next; it will get you to the airport sooner.
If you take the S1 to the airport be aware that the train splits at Neufahrn, with only the back end going to the airport (the front goes to Freising). The cars should be marked with their ultimate destination.
If you leave from Marienplatz, the S-Bahn in opposite directions leave from different levels. The S1 leaves from the lower of the two S-Bahn levels (Gleis 2), but there is only a one minute window out of 20 minutes in which the S-1 will get you to the airport sooner. The other 19 minutes, the S1 will get you to the airport sooner, so my advice is just to go directly to the upper station (Gleis 1) and take the S8.
If you are going directly to the US (no stop in another country), you will probably leave from Terminal 2. However, if you are flying on United, their gates are on the far south end of T2. It's a long hike from the entrance, security, and Schengen.