You'll hear lots of talk about crossing Lake Titicaca from Peru to Bolivia via hydrofoil or catamaran. At this time you can not go completely across without stopping at the border and walking from Peru into Bolivia or vice versa. You can still use hydrofoils and catamarans in your journey to Bolivia's side of the lake from Copacabana on the Bolivian side, then on to the Sun and Moon islands for an overnight or two on Sun Island.
Copacabana is a pleasant, if touristy, town which provides easy access to the lake and the surrounding countryside. It's also a major pilgrimage destination for devout Bolivians at Easter and lost South American hippies all year. The breathtaking Moorish-style Cathedral, built between 1610 and 1619, is where you'll find the striking sculpture of the Virgin of Copacabana. If you see decorated cars lined up in front of the cathedral, the owners are waiting to have them blessed. You can combine your visit with the semi-scramble up past the stations of the cross on the hill above the town. If the climb doesn't knock you out the view will.
At the Inca Utama Resort & Spa at the Huatahata harbor you can spend a couple of days relaxing and visiting the Andean Roots Cultural Complex. The observatory with a rollback roof gives you a view of southern-hemisphere stars through powerful telescopes donated by NASA.
Bolivia's unit of currency is the boliviano—though Bolivians often refer to their currency as pesos. The exchange rate is about S/1 to (B)2.6.
Bolivia now requires U.S. citizens to obtain a visa to travel in the country. For a price tag of $100, the visa is good for up to 90 days in a calendar year. The application can be done by mail or in person at any Bolivian Consulate, not by the Internet. Additionally a yellow fever vaccination certificate is also necessary to show upon entry. At this writing, you were allowed to pay a US$100 fine for not having a visa and get into the country. How long this will last is anyone's guess, but you could always give it a try.
If you're taking a bus from Puno, three hours into the ride the bus will stop just after Yunguyo for border-crossing procedures. Most higher-end bus services hand you immigration forms on the bus. As you leave Peru you'll get off to get an exit stamp from the Peruvian immigration, and then walk through to the small Bolivian immigration building, where you get an entrance stamp and will have to show your visa. From there you catch up with your bus, which will be waiting for you. Keep all immigration documents, your passport and visa safe; you may need these when leaving Bolivia.
The border-crossing tours have packages from US$150 to US$400. Reputable agencies include Crillón Tours and Transturin Ltd; based in Bolivia, tours go from Puno to La Paz and vice versa. Both include a pick-up from your hotel in Puno, transfer by first-class bus to the border in Yunguyo (a three-hour drive). After crossing the border you take a bus to Copacabana, a funky beach town (30 minutes). The most expensive—and comfortable way—to get to the Isla del Sol and Isla de la Luna is by hydrofoil from the Inca Utama Hotel but cheaper boats leave from Copacabana all day. The journey takes about three hours and costs (Bs)30. Once you are on the island, it's walking all the way.