I'll compare two methods. The first one I'd been using for a long time; the second one I found recently. I recommend using a combination of both.

BBC method (YouTube video, 2:04):

• In the video Ms. Hornby uses salt. It works almost as well without salt.
• It looks like she's using flaky sea salt. (I'm not entirely sure, though.) Coarse salt works even better.
• This gives you total garlic goo, which means maximum allicin production.

YKOStudio method (YouTube video, 6:58, skip to important part)

• Quicker and less messy than the BBC method, but more brutal.
• Doesn't give you the nice goo, just fairly small pieces and some juice.
• If you want goo, peel and crush the garlic according to this method, then mash it like in the BBC video starting at 1:13. You can leave out the salt.