Piriapolis lies about 80 km east of Montevideo and frequent buses, many of which go on to Punta del Este, connect the two. The bus station in Piriapolis is about 4 blocks from the beach and within easy walking distance of the youth hostel and most of the hotels. If you are trying to get from Piriapolis to anywhere not along the coast you'll most likely have to return to Montevideo first as most bus routes go from the capital.
From the airport near Montevideo, it is about an hours drive to Piriapolis. You follow the Interbalnearia to the Piriapolis exit. From the exit to the city it is another 10 miles. You will have to pay 2 tolls ( local currency) on this route.
The car rental offices are at the airport as you leave the building.
There are buses that leads you from one part to another; of course, you can drive your car or ride your bike, but hitch-hiking is a common way of "traveling" during summertime.
Hay buses que te llevan de un lugar a otro; por supuesto, puedes conducir tu auto o montar tu bicicleta, pero "hacer dedo" es una forma común de viajar durante el verano.