Doesn't emacs already have that built-in? This isn't slime-specific at all...
C-x b RET (and repeat it again to come back, as many times as needed)
I use this extensively...
And of course if you want to compare differences, C-x 2 or C-x 3 might be the thing for you. C-x 0 to kill the current "window", C-x 1 to keep only the current "window" (going back to "full-screen mode")...
You might want to have a look at the Emacs manual for "Windows":
C-h i (to access Info)
d (to access the Directory node, if not already there)
m Emacs (to access the Emacs manual from the menu)
m Windows (to access the chapter on windows from the menu).
From within Info, press H to access the info tutorial for basic
commands on how to use Info, it's a necessity to learn Emacs properly and many Unix tools have their main documentation in Info...
Hope this helps!