How to save a list of all the installed packages in Emacs 24?

The canonical methodology is the best (described by ataylor). Here is a more clumsy method.

M-x list-packages. C-s installed till you find the first row of installed package. Start selecting with C-SPC. Go down till you reach built-in packages. Copy with M-w. C-x b for new buffer. Paste with C-y.C-x C-s to save file.

Only advantage that I see is this is a tad more descriptive. Showing a small description of your packages. useful when you install some packages and forget about it.

You can get a list of currently installed packages (excluding built in packages) from the variable package-activated-list. To automatically install them on startup, see this question: how to automatically install emacs packages by specifying a list of package names?

More specifically, if you do C-h v package-activated-list, copy the value shown, and insert it as the value of prelude-packages, emacs will automatically ensure those packages are installed on start up.