You can get a ticket to tour Neuschwanstein or hire a guide from the ticket center in Hohenschwangau. Get there early, as there are limited tickets for each tour. A ticket for a 35 minute tour of the interiors of either Neuschwanstein or Hohenschwangau castle costs €12 (2012 price), a "Royal" ticket to tour both costs 23 (See Information for Visitors on the official Neuschwanstein site). If you stay at a hotel in Hohenschwangau like the Hotel Muller (recommended), the hotel staff can help you get tickets.
You do not need a ticket to walk up and view the castle from the outside. The pictures in this series were taken on a walk that took about two hours total from the hotel Muller, including time to take pictures. It takes 30-40 minutes to reach the castle from below.
You can get a horse drawn carriage in front of the Muller that will take you near Neuschwanstein castle for around €6 up and €3 down.