By plane: The easiest way to get from Munich airport to Regensburg is the airport shuttle service (prices can be seen here). Please note that the web page says: "You should book your shuttle 2 days in advance. We can only accept your last-minute bookings if we have vacant seats in the pre-booked vehicles."
Alternatively (and for a lower fare), you can get from Munich airport to your hotel by bus and railroad. Buses go from the airport terminals to Freising railroad station every 20 minutes. Trains from Freising to Regensburg run at least every 60 minutes; the detailed schedule and fares can be found here (select start "Freising Bahnhof" and destination "Regensburg"). The ticket can be bought at Freising station or online (you must print the online ticket on paper prior to your journey). See below ("By train") how to get from Regensburg station to your hotel.
By car: All relevant locations (hotels, ...) are indicated on the Conference Map. Click on the "Get Directions" link in the upper left corner, then on the link of your hotel (Apollo or Kaiserhof) in the menu to the left. In the speech balloon which has opened now, click "Directions". Then type the start of your travel into box "A" and click the "Get Directions" button. You will obtain a list of suggested routes.
Hotel Arch lies in a pedestrian zone where car traffic is in general not allowed. (This means that route-planning software refuses to make suggestions how to get there.) If you are accommodated in Hotel Arch, you can unload your luggage at the hotel, but you will have to go to a public parking garage afterwards. This web page explains what to do.
By train: Train schedules and fares can be found here. Tickets can be bought at railroad stations or online (you must print the online ticket on paper prior to your journey); in IC and ICE trains, they can also be obtained for an additional fee from the ticket collector.
After your arrival in Regensburg, leave the railroad station through the main exit. You can go to your hotel by taxi (to the left of the main exit); or by bus, as follows. If you are accommodated in Hotel Apollo, follow the path to the bus stop "Albertstraße (to university)" which is indicated on the Conference Map; take the bus line 6 to "Klinikum", get off at "Neuprüll". If you are accommodated in Hotel Arch or Kaiserhof, go to the bus stop "Maximilianstraße" and take the bus line A "Altstadtlinie"; get off at "Domplatz" for Hotel Kaiserhof, get off at "Haidplatz" for Hotel Arch. Tickets are available from the bus driver, the fare is 1.90€. If you are accommodated in Hotel Arch or Kaiserhof and your luggage is not too heavy, you might even prefer to walk.
The registered participants will be accommodated in Hotel Apollo (near the university) and in the Hotels Arch and Kaiserhof (in the city center). The Conference Map shows the locations of the hotels and how to get from there to the conference by bus.
Hotel Apollo lies within walking distance (approximately 1.1 km) of the math building, but you could also take the bus line 6 from "Neuprüll" to "Universität Mensa" to reduce the necessary footsteps. Consult the Conference Map for details.
From Hotel Arch or Kaiserhof, take bus line 6 or 11 to "Universität Mensa"; click on the bus stations in the Conference Map to get detailed information. Tickets are available from the bus driver, the fare is 1.90€. From the bus station, walk along the subterranean street to the math building (cf. the Conference Map), then take the stairs (either outside or inside the building) to get to the main floor (one floor up from street level).