We're going to let pictures do most of the talking about this sacred island in Lake Titicaca, but we wanted to add a few notes on logistics (prices as of early October, 2013):

The bus from Puno will probably drop you off in the middle of town in Copacabana. You can buy the boat ticket to the island from one of the tour agencies there or walk to the pier and buy it yourself. The price was 20 Bolivianos (Bs) per person for the trip to the south end of the island.
You can choose to head to the north or south end of the island. The south end has more accommodation and dining options and will be a better base if you're only staying one night.
When you get off the boat, you have to pay an entrance fee of 5 Bs per person before stepping off the pier.
You will be bombarded by hostel/tour offers when you get on land. We paid 25 Bs per person to share a triple with our friend Alvin (a traveling buddy from the trek to Machu Picchu), but all the beds, regardless of single, double, or triple rooms, were 25 Bs per person where we stayed. It was fine for a night.
In terms of what there is to do, there are plenty of ruins scattered on the island, mostly to the north. You can boat or hike to the north and both have associated costs. There are checkpoints on the hiking path you have to pay to pass, but we can't tell you what they cost: we got lost when we did the hike and did some backwoods trekking before we found a local to follow back to a point on the path after the checkpoints.
When you get to the bay from which you get your first view of the town at the north end of the island, you may get someone offering a boat ride across the bay. Our rowers promised it would save us time (see #5), so we took it for 30 Bs. Not sure if it really does reduce hiking time, but it was a nice way to enjoy the bay.
If you plan to hike to the north of the island and then boat back the same day, leave plenty of time to visit the ruins if you want to see them. We missed out on the ruins (see #5 above) but were able to have lunch on a bluff looking towards the Cordillera Real.
The boat from the north end of the island back to Copacabana was 25 Bs. There's a little shack selling burgers near the pier that is pretty good and is 10 Bs per burger for meat, avocado and tomato.
Copacabana wasn't that interesting for us. Accommodation is either expensive or not great or both. The top eateries were also closed for the short time we were in town, but we had a good brunch at one of the restaurants on 6 de Agusto. It was across the street from La Orilla and up the hill one or two buildings.

Enough with the words:

The view of the Cordillera Real from our hostel

Cute kittens at our cheap-as-chips hostel

A local boy and his radio. He taught Tyler some sweet dance moves

He had to stand on the wall to get the radio to pick up the best stations

Main square of one of the small villages on the island

The coast along the northern part of the island

Rapturous Rajasthan

Isla del Sol - Home of the Incan Sun