Every morning at 8:20am a boat leaves from Puno. It takes about 4 hours, including a ~45min stop on one Uros island. It is a "multiple way" ticket (Puno-Uros-Amantani, Amantani-Taquile the next day) that you can buy directly at the port for 30s.
In the morning there are direct boats from the island back to Puno, but you can also opt for the boat to Isla Taquile, with a few hours break to explore that island as well. This boat is the same as the one you probably took the day before. It leaves at 8:00am, arrives in Taquile at 9:00am, and leaves Taquile at 12:00am, returning to Puno at 3pm.
Note that when you buy the multiple way ticket you can stay longer in Amantani if you want, just keep your ticket and take the boat to Taquile anyday (check when buying the ticket though).
There is a 8s entrance fee to the island.
Be sure to bring extra money as your host family will try to sell you some handmade clothes.
Electricity (except some houses with solar panels) is not yet integrated in the village, so a flashlight is handy to get around after dark.
Hike up pachatata or the slightly higher pachamama. Both offer superb views and ancient ruins. On pachatata there is a small museum as well as a temple (closed for public), which is still used for ritual offering. On pachamama there is small ancient tower, climb up for a 360° panorama, and another temple. Plan on hiking to the pachamama in time to see the sunset; it is a spectacular setting, but as soon as the sun disappears, it can get awfully cool ( even by Canadian standards) so take a jacket. Your hosts will often have typical Peruvian toques to lend you or otherwise you can buy one- they are very cheap. A profound way to visit the island is to do a silent meditation retreat. Meditation Retreat Peru offers monthly 5 day silent meditation retreats on the island Amantani. They are usually offered around full moon.
There is no restaurant in town, but food is included in the accommodation. There is a small shop selling snacks, candies and the like.
Every night there is a party, specially organized for the tourists. Locals will lend you their colorful clothes and try to teach you their local dance.
You can buy beer here for 10-12 soles (~600ml bottles).
About 50 families have accommodation for tourists. To give everyone a fair share of tourist dollars, tourists are assigned to a family on a rotational system. So one does not have much choice where to stay. The accommodations are basic but usually nice, and include tasty lunch, dinner and a breakfast. The price is 45 soles per person including food (March 2016).
The boat going to Taquile and then Puno leaves at 8:00am.