If you've booked the Germany
ABD, then you will visit Neuschwanstein on the very last day of your trip. ABD takes you there by private motor coach. Your tour of the castle will be exactly the same as if you visited there on your own (it is not a private tour, and there may be non-ABD guests with your group). There is a shuttle that takes you up the mountain, reasonably close to the entrance, although there is still some walking. At the end of the ABD tour, you are treated to a "special" trip back down the mountain (I won't say how, because the guides like to think that it is a surprise) and lunch at a nice restaurant/hotel.
If you opt to do the tour on your own, you can take the train to Fussen, and then make your way to the castle. I have no idea how far in advance tickets sell out. If you go on your own, I highly recommend doing the tours of Hohenschwangau and Neuschwanstein (there is not time to do both if you go with ABD). Also, you can opt to walk all the way up the mountain, from the ticketing area to the castle. If you are able, I highly recommend this, as well, as it is a very scenic walk.
Depending on when you visit, the weather may be less than ideal. We were there last year in mid-June, and the temps. were in the 50s and it was foggy and rainy!
I have also visited Herrenchiemsee castle, which is on an island in the middle of Lake Chiemsee in the town of Chiemsee (about 60 km southeast of Munich). This castle was built by King Ludwig II, who also built Neuschwanstein. Herrenchiemsee was also never completed, but it is still a lovely place to visit. I especially enjoyed the journey to get there, as it involves a train ride, a walk through town to the ferry, the ferry ride, and then a walk on the island.