How do you copy and paste into Git Bash
Press Insert.
Also, to copy from the window, try clicking the console's window icon (topleft) and choosing Edit -> Mark, then drag a box on the text, then press Enter. (You can also paste via the window icon menu, but the key is faster.)
UPDATE
Starting from Windows 10 the CTRL + C, CTRL + V and a lot of other feature are implemented in conhost.exe so they should work with every console utility on Windows. (You have to enable Properties -> Option tab -> Quick Edit Mode)
Aside from using the edit menu commands, you can directly paste into the git bash window using the keyboard shortcut, Insert.
It's not really a function of git, msys, or bash; every windows console program is stuck using the same cumbersome copy/paste mechanism for historical reasons. Turning on QuickEdit mode can help -- or you can install a nice alternative console like this one, and change your git bash shortcut to use it instead.