how to send someone a website you built ?

Typically you would:

1) tell them to setup their hosting and provide you access to deliver the site there (alternately they can give you their credit card info and you can set it up for them)
2) manage the hosting and bill for it
3) just send them the files and they can handle deployment to their server

What you should do in this case really depends on your situation.

First off, thanks for that nice, concise numerical list.

Might I ask: What is the “access to deliver the site there” you mentioned? Is it just the other person’s hosting account username and password ?

Also… say you’re redoing a website for someone, and they already have their hosting set up. In that case, do you normally ask for their hosting account username & password, and then just take down the old site and put up the new one ?

The access is usually an FTP login, but sometimes you'll need the hosting account login in order to setup databases etc (if the site is not static files only).

As for the second question, typically in small-scale web development that is the case. Ideally things could be revision controlled and backed up etc but what you describe is the typical case for most web developers. They might, at most, just copy the old files to an "old" folder on the web server for the client.