The name is misleading but it has stuck in everybody´s mind, the gardens are not floating at all.
Chinampas. This is the proper name of the parcels where people grow from vegetables to flowers all year round (the area is extremely productive, with as much as 3 crops a year).
The word comes from the Nahuatl word chinamitl, meaning "square made of canes." A chinampa is an artificial patch of soil, a man made island, it starts with a wooden barge that is steadily filled with soil until it slowly sinks to the bottom of the lake, in the sinking process the "walls" of the parcel are kept above the level of the water by adding more canes on top and more soil. The lake was never too deep so it´s not a difficult process. The idea was to make some landfill without killing the lake at the same time, and also having a very fertile parcel with full access to a year-round supply of water.
The trip. You go to one of the several docks embarcadero available and agree with the driver a price per hour (last time I was there it was 140 Mexican pesos (2005) for one hour, in a 12 passenger boat (blue roof). The boats are called trajineras and are driven like the gondolas in Venice by a guy pushing on a large pole.
During your trip you have a view of the parcels and some greenhouses, in the touristic area is mostly flowers or plants to sell, you normally don´t go to the orchards unless you specifically ask for that. In the main channel which is very wide you will find musicians (mariachis, trios, duos) to sing for you (it was 50 mxp per song in 2005) they may travel in their own trajinera, boat or just transfer from boat to boat. The trajineras are all roofed and decorated with fake flowers and each has a woman's name, if you are lucky you may find the one you like. Inside the trajinera there are benches alongside all the boat and tables in the middle for you to throw a party or enjoy a picnic, you can bring your own food or buy at the many trajineras that sell all kind of food from corn on the cob, quesadillas, tacos to pollo con mole and arroz. Beers are easily available.
To arrive you have many options, the cheapest is to take the subway and transfer in Taxqueña station to the "A" line which uses trams on rails to get to Xochimilco, ask which station is more convenient to get to the dock you choose. It may take you an hour or 1:20 min. to get there from Polanco or Downtown. By bus, take any going directly to Xochimilco (ask the concierge at your hotel) or if Periferico is near, take the one heading south and transfer in Villa Coapa. By taxi, don´t worry on the way back, there are many safe taxi hubs.