I’ll mainly answer the ‘how do I get to Marktoberdorf’ part of your question.
The easiest method is by rail and generally you have two slightly different options. The train station of Munich airport is somewhere between the terminals. It is marked by train signs and, as you get closer, by a white capital S on green background (the symbol of Munich suburban trains). The underground platform can be accessed by elevator or escalator.
Two suburban lines service the station: S1 and S8. Both call at the central station (Hauptbahnhof) which is Munich’s main train hub. The S8 also calls at Pasing station, a secondary hub for westbound trains out of Munich (which includes Marktoberdorf).
If you decide to change trains at Munich central, you will need to make your way from the underground suburban train platform to one of the platforms 27–36. Follow the signs to long-distance and regional trains (there are escalators). Once you arrive in the big station hall, face the trains, locate the rightmost platform (number 26) and walk along it to reach platforms 27–36. This is where trains to Marktoberdorf typically depart from.
Every two hours there will be a direct train Munich–Füssen which calls at Marktoberdorf. If you’re lucky and can immediately take one, go for it. In the hour in-between, you will need to look for a train to Kempten(Allgäu) and transfer in Buchloe. If you ask the ticket machines or the DB website they will tell you to change trains in Kaufbeuren. Do not do that, change in Buchloe instead! In Kaufbeuren, you would need to change from platform 1 to platform 3 which involves taking the tunnel under the tracks which is only accessable by stairs. In Buchloe, one stop before Kaufbeuren, you leave the train bound for Kempten, wait at the platform and board the train bound for Füssen either at the same or the opposite side of that same platform. Furthermore, platforms in Kaufbeuren are 16 cm above track level, meaning you need to step far down, while those in Buchloe are 76 cm, meaning that you can step out evenly.
Your second, slightly different option involves catching an S8 out of Munich airport and taking that until Pasing. You will arrive at platform 8 in Pasing and need to change to platform 4 for your train bound for Füssen or Kempten. Since Pasing is a much smaller station, it is easier to change trains here. Escalators and elevators are provided at each platform. From Pasing platform 4 on, the same applies as did above for Munich central.
The ticket price is €23. You are looking for a BayernTicket, which is the cheapest fare for a single person. It is valid for the entire trip from the airport to Marktoberdorf (and in local buses in Marktoberdorf, too, to the best of my knowledge). Every additional person costs an additional €5. It can be bought from the ticket machines at Munich airport station. Have a pen at hand and fill in your name in block letters. (If the conductor has a bad day he may fine you for not having entered your name. It has happened.)