I just ordered my MYLR, but I've been doing electrical work for a long time... There is a LOT of correct, and incorrect info in this thread. First of all, don't trust anyone on the internet blindly. Talk to/hire an electrician. With that said, here's correct info:
Wire must be rated at or above the branch circuit protection device. (Circuit breaker). Longer runs require bigger wires due to voltage drop. Anything less than 50' can generally use 6awg.
Specific to 6awg NMC (Romex) is rated to 55a due to wire heating/National electric code (NEC). This limits it to a 50a breaker. If you want full rate charging, you must use a minimum of 2x 6 AWG THHN (90c rated) copper (hot wires, red and black, or both black) and 1x 10awg ground (Green, must be 8awg per NEC), that is rated at 75a, on a 60 amp breaker. This will all fit into a 3/4" conduit( ANY kind), but 1" is much easier to do. Use stranded wire, not solid. These limits are because the maximum designed branch circuit load shall not exceed 80% of the protection device rating for these kinds of loads (Appliances/Motors etc)
You can run 4 AWG NMC (Romex/Service entrance cable - as long as it's copper, NO aluminum, the charger is not rated for it) or THHN. 4awg NMC is 60c rated @ 70a, and THHN is 90c @ 95a
In most places you need a permit as well.
If you don't fully understand what your are doing, HIRE AN ELECTRICIAN TO DO THE WORK! There is a lot more to this than just running wire and plugging it in due to wire size, conduit, routing/wire protection, where you can/can't drill holes in structural hose members etc. It's not worth burning your house down if you get it wrong.