The entrance to the fort is located on the extreme end of Leme Beach (near Posto 1), and costs R$4…read moreto enter. The fort and surrounding area are owned and operated by the Brazilian Army, so what you have is a natural area that's clean, safe, and beautiful.
After entering the complex, follow the signs that say "visitação do forte" and walk up a long (and a bit steep) brick road. Along the way you'll see lots of wildlife, including monkeys, lizards, birds, and butterflies. There are markers along the walkway that explain the history of Leme Hill (Morro do Leme) and the fort. The fort is at the top and is pretty well preserved, with a few art exhibits and views of Pão de Açúcar, the Atlantic Ocean, and Copacabana that can't be beat. It also explains some of the military history of Brazil and the role the fort played in a few of the revolutions. There are howitzers on the top which have been maintained very well, and a scope which is free of charge. Someone has been feeding the monkeys up there, because they are extremely tame and will let you get very close - but be careful, I've heard that they bite.
The "hike" up should only take 10 min or so, and the entire visit is definitely worth a trip. Not many people seem to know about the fort, so it seems a bit underutilized and therefore not crowded.