Pace yourself and hydrate
You'll likely be walking under a broiling tropical sun surrounded by a sweaty (if friendly) crowd, so bring water to keep yourself hydrated, and don't be afraid to break off from the procession; it's slow moving, so you can always catch up.
Go early or return later
To really appreciate Borobudur, one of the wonders of the ancient Asian world, visit after or before Waisak to avoid the crowds.
Raise a sky lantern
Thousands rise up in to the night sky symbolizing enlightenment for the entire world.
Add a second temple to your trip
You should also check out the nearby ruins of Prambanan, a Hindu temple complex that is nearly as impressive as Borobudur itself, topped with an eye-goggling 154-foot central building. Besides being an impressive piece of architecture in its own right, Prambanan is not nearly so crowded as Borobudur.
Dates
Waisak is celebrated on the full moon in the 4th month of the Chinese lunar calendar and Waisak is a national holiday in Indonesia.
Lodging
By far, the logical place to base yourself is the city of Yogyakarta, which happily is also one of the most livable, easy to love cities in Indonesia. "Yogya," as it is commonly called, is heavy with students, arts, culture, food and a relaxed vibe, and has tons of accommodation serving all budgets and tastes. It can be accessed via either a short hop flight or (roughly) 12-hour bus or train ride form the capital of Jakarta.