Hitting the double quote in command mode tells vi that the next letter you enter is going to be the name of the buffer that you'll be refering to. For instance:

"aD

will cut everything from the cursor to the end of the line, and throw it in buffer a. To paste it in again, you'd say:

"ap

The :map command binds a key to a macro... like so:

:map q xp

which will make the q key cut the letter the cursor's presently on and paste it after the next one, effectively transposing them.

Some of the other things you mention make me think. It's about time I went back and learned some more stuff, to make my editing more pleasant. It's easy to just roll along after a certain point, using what you know.