this used to be a little weird, and should now pretty much just work the way you would expect
To copy text, just select it and hit Ctrl-C (Command-C on a Mac). If the selection disappears, that's normal and it means it's worked.
To paste, use Ctrl-V (Command-V on a Mac).
If you're on Linux, you should also find that the middle-click paste buffer works just fine.
Pasting multiple lines will now work fine in both Firefox and Chrome
Copying multiple lines works fine in Chrome, but in Firefox it sometimes ends up munging everything onto a single line when you paste it again.
How to send ^C or ^V to the console
To send the actual Ctrl-C (^C) characters to the console, just hit them as usual when you have nothing selected. Ctrl-c will only do a copy action when you have console text selected.
To send a Ctrl-V (^V), use Ctrl-Shift-V.