Xochimilco is to the south of Mexico City, and gives a glimpse at the effects of rushed urbanization over the years. It's a great place for tourists - not only to ride the canals, but to explore a smaller village outside Mexico City.
Though Xochimilco is far from the city center, it is a relatively safe & easy 90 minute trip from the city center using public transportation. First, take Metro Line 2 (the blue line) to the end - station Tasqueña (you may also see it spelled Taxqueña). As you exit the train platform through the turnstiles at Tasqueña, head through the doors straight ahead of you to get to the Tren Ligero (light rail). The light rail does not accept Metro tickets, so you must buy a CDMX re-loadable card (you can share one card between multiple people) for $10 and load it with $3 per-person one-way at the booth just outside the train turnstiles. You will take the light rail to station Xochimilco, the last station on the light rail line. The embarcaderos are only a 10 minute walk through the village: follow the small blue signs on the street with arrows that will lead to the embarcadero, or just follow the crowd. There are several entrances to find a trajinera, so don't worry too much about going the the right one.
At the embarcadero, take one of hundreds of boats (trajineras) through the canals which is all that is left of the lake on which Mexico City was built. This activity used to be widely enjoyed by Mexicans and it used to be one of the more authentic tourist experiences available. Nowadays however locals no longer consider it a nice experience because of the decay in some areas, and it is at risk of losing it's UNESCO heritage status. The boats are colorfully painted and often bear the name of the owner's female child or other relative.
There are set prices depending on the size of boat and length of the ride, though if you speak basic Spanish this can be bargained on. It seems like you can expect to pay $350 for a one hour ride for 2 people. You can bring your own food and drinks for a picnic lunch on the larger boats, as they have a long table down the middle. As you travel down the canals, music boats float by with bands, mariachi trios, and marimba players, and for a fee you can have them float along beside you and play the songs that you request. As you travel you will see city life, houses ranging from run-down to amazing villas, restaurants, and greenhouses where flowers and plants are grown. Further beyond the city canals there is a wildlife preserve in which the original character of the chinampas (Aztec-era "floating gardens") may be seen.
Along the embarcadero, there is an overpriced souvenir market with handcrafts, T-shirts, embroidered clothing, linens, sandals, and other souvenirs. In the off season, not all of them may be open. In addition, you will approached on the street by walking vendors. Also, across from Xochimilco Cathedral is a plaza where one can buy more handicrafts (as well as not-so-great second hand clothing imported from the US)
The best merchandise is available at the amazing roofed public market, Mercado de Xochimilco, Avenida Nuevo Leon s/n Santa Crucita, Xochimilco, . This is worth a visit to Xochimilco alone - it is where the locals shop. It's two square blocks and slightly busy, but not too packed. Here you can buy produce, dried chilies, ice cream, juices, meat, fish, and clothing and items for baby bautizas (baptisms) such as elborate christening gowns, floral displays, and items relating to the child's patron saint. If you are lucky, you may be able to pick up some blue corn tortillas or patas (spiced, jellied cow's feet.) edit
On the canals, there are some trajineras which sell sweets, tacos, boiled corn or roasted corn on the cob. There are also "restaurant boats" selling simple meals of rice, chicken in sauce and tortillas. Vendors also stand on the shore in some places selling meals, drinks, candy, and ice cream to boats that float by.
In downtown Xochimilco, there are several areas of the market with food stands, as well as restaurants outside the market(several pizzerias and taco restaurants nearby). Keep your eyes open when walking to the embarcaderos - there are many places all along the village.
Generally, there will be a bucket of soft drinks, fruit drinks and beer on the boat; you pay at the end of the boat ride for what you consumed. Soft drinks and beer may be also purchased from vendors who float by in their own boats; a simple hand signal is enough to get them to come over. Some vendors also set up coolers on the banks. As with all food purchased on the canals, it helps to have exact change or close to it.