You can plug a Tesla into most outlet types in the US.
While you can charge it with a regular 15 amp 120 Volt outlet, it can provide a maximum of 12 amps (always derated by 20% by electrical code), or 16 amps if using a 20 amp circuit.
But, if you go to 240 volt outlets (or add one), it can charge at a much faster rate. For general usage, I would recommend a NEMA 14–50 (240 volts, 50 amp circuit breaker) for 40 amps maximum or a NEMA 14–60 (240 volts, 60 amp circuit breaker) for 48 amps maximum charge rate. The NEMA 14–50 is the most common high power outlet, and most RVs and clothes dryers use this today as well.
Total watts is amps times voltage, so that gives you the maximum charge rate.
On the other hand, you can have a Tesla Wall Connector installed. It runs about $500 plus installation. It has some advantages over an outlet, but I think using a NEMA 14–50 or NEMA 14–60 outlet is the better, more general solution.
Edit:
As of May 2022, Tesla is charging $200 for the portable EVSE (called a “charger” by many people, even though it is not - the actual charger portion is in the car), which was previously free with a Tesla purchase. Alternatively, they are offering the Tesla Wall Connector for $400. It’s not clear if these prices are for purchase with a car, and whether only 1 can be purchased at those prices.
Also new information from Tesla indicates that you should normally leave your car charged in and set to 90% charge, and ideally use the charge to no lower than 40% for longer lifetime and range of Tesla’s batteries. Prior to this, keeping the charge the least amount of time outside 20% to 80% was the basic guideline.
However, when on long distance travel, your faster charging is to run the car to about 10% and then quick charge up to about 50 to 60%, or enough to get to your next charging stop. So many quick charges are get you more range than 1 long charge for the same time. So that is contrary to the 40% to 90% guideline. It is probably OK for the trips though.