Unless your state has a law, you can do it. Watch YouTube videos. I did it in one hour. Buy 02 wire, 4 conductor, red, black, green, white.
Buy 14.50 box and plug at HD.
Depending on home service ? 100 or 200 amp? You get 50 or 100 amp double breaker.
Dont need conduit in garage in most staes.
A 14-50 must be used with a breaker 50 amps or less; I think he was referring to the overall service to the house. Most likely you'll have trouble if the whole house only has a 100 amp service and you're trying to add another 50 amp load to it. I had to upgrade to a 200 amp service (from 125) in order to add a 14-50. Fortunately, the feed from the utility to my meter was already sized for up to 225 amps, so the panel upgrade was local to just my house and I didn't need to dig up the wiring to the pole / street. Other houses on the street don't appear to be so lucky.
Also, #2 wire will NOT fit into the 14-50's screw terminals. #4 is as big as you can use with them, and #6 is all you really need unless the run is exceedingly long, or if you plan on upgrading the outlet to a hardwired EVSE in the future. I put in #4 for the later reason - crawling under the house to string wires is annoying enough that it was worth spending the extra money now. But do note that #4 is a whole lot harder to work with than #6.
Bottom line, yes, in theory you may be able to do this yourself (do get the proper permits from the city for CYA purposes), but you really should have an electrician and the electric utility look at the situation for any gotchas. Not all are visible unless you know all the questions to ask. What I recommend is to find an electrician who will let you contribute "sweat equity" to the project to save money, and let him/her do their thing in terms of making sure everything is done right.