If I sell a domain, get money for it, and want to give it to someone else, how would I do that? Would I just give them the EPP code and let them transfer it?
Depends on the registrar itself... they all follow the same process but could be different at the same time
Besides, some registrars alllow you to "push" the domain, what means that you can transfer the ownership to other person who has an account with the same registrar at which you registered your domain. Push is easier since only requires that you receive the payment to send it straight to the other person without EEP code.
Well I don't know yet, but I don't have a well known host, so I would expect a push wouldn't work. (Registered through fastdomains, don't think that's good either)
if the buyer using the same registrar, you often can push to the buyer account without the transfer process. At godaddy this is under "Account change" button for example The same applies if you sell your domain via 3rd party, e.g sedo. They have accounts at all major registrars and you can push your domain to them without transfer as well