Desaguadero is a border crossing between Peru and Bolivia. It is the main crossing on the route from Puno (and Cuzco and Arequipa), Peru and La Paz, Bolivia. It is a landlocked town with no access to Lake Titicaca. There is a second border crossing at Yungani leading to Lake Titicaca at Copacabana, Bolivia: to reach it, take the right branching road approximately 10 miles before Desaguadero.
There is no reason to linger in Desaguadero. Be aware that if you need to buy a visa (as U.S. citizens do: it's $135 in dollars), there is no ATM in Desaguadero.
The time in Peru is one hour behind the time in Bolivia (11am in La Paz is 10am in Puno)
Grab a van from the La Paz cemetary 'terminal'. One street west of where the buses leave for Copacabana. Tell your taxi driver "Quiero ir a Desaguadero" and they'll drop you at the right spot. Buses begin to leave early in the morning and stop mid-afternoon. Make sure you have warm clothes because it can be cold waiting for the bus to fill up.
It's a five minute walk to the border from where the buses let you off. Random taxi dudes will try to take your bags off the van and force you to use their taxi. Obviously, don't encourage this kind of behaviour and demand your bags back. Go with another less unruly taxi driver if your bags are heavy.
Once across the border, you can get a nice new van to Puno. About 2 hours drive.