tegelberg luge

There are buses, about once per hour, from Hohenschwangau Haltestelle, just around the corner from the ticket kiosk, to the Tegelbergbahn. Most take about 5-15 min.

It's essentially the same bus that comes out from the Füssen Bahnhof to the castle; it just continues on. Here's the schedule.

You can also find that information on the German Rail website. Put in "Hohenschwangau" and "Tegelbergbahn" (it will give you choices; select "Hohenschwangau, Schwangau (Schlösser)" and "Tegelbergbahn, Schwangau"). You can also start at "Fuessen Bahnhof".

We (family of four) walked from Neuschwanstein to Tegelberg last summer. The walk was mostly pleasant; I'm guessing between 1 and 2 miles. The hardest part was finding the right trail. The one we took through the river gorge worked, but others might work also. The walk along the river was very pretty and mostly easy, except for an odd narrow walkway over the water that was too crowded at the time we were crossing (I don't think it was meant for two way foot traffic). Once we got away from the river, the path was flat and not well marked, but we could see the Tegelberg gondola, so we just walked toward it.