I first attempted installing GHC 7.4.1 from the prebuilt x86_64 binaries provided from haskell.org/ghc but they are linked against an old version of libgmp, and rather than try any ugly symlink hacks*, I decided to try compiling from source, which I've wanted to do for a while anyways. Luckily the process is quite simple due to the miraculous work put into the build system.
I like to install everything locally in my $HOME/src/ghc so that it is easy to remove everything later on down the line, but pick your own poison. Also, it is necessary to use cabal-install from darcs HEAD because the current stable version on Hackage is not updated for GHC 7.4.1. You will need > 3GB free space for this process and a healthy amount of RAM.
And you're off to the races!
Update 2: As hvr_ pointed out in the reddit comments, it is possible to get around the libgmp easily with a
sudo aptitude install libgmp3c2to avoid recompiling GHC yourself. So you can go that route as well but you'll still need the latest cabal-install.
Update 3: To avoid much pain later on when trying to build profiling libraries with cabal-install, I have added the step of exporting the EXTRA_CONFIGURE_OPTS variable on line 19 before running bootstrap to generate those initial profiling libraries as well.