For a DIY day trip to Xochimilco's canals, you can get there by using public transportation (though…read morethe journey is long and may require a few transfers), or taking an Uber.
If you're not going to Xochimilco on a guided tour, you'll need to hire your own trajinera, or boat. The current going rate for a boat is 600 pesos per hour.
Embarcadero Cuemanco is where we went. Apparently Nuevo Navitas is more of a party scene, which I didn't realize, but then we got the whole it's closed scam and our uber driver started taking us somewhere else which is apparently an even bigger scam. If you go to Embarcadero Cuemanco you can ask them to stop at the axolotyl place, it was cool to see the little lizards and they had bathrooms (10 pesos) too.
A really nice way to spend a few hours!