Suppose your current branch is master and the old commit is a1b2c3, then you can change all the files in your working tree back to the old commit with:
git checkout a1b2c3
… and return to master with:
git checkout master
This way of hopping about in your git history (i.e. checking out a commit with its object name, also known as its hash or SHA1sum) is very useful for finding a previous good commit for git bisect, for example, since it won’t move your branches.
One thing to bear in mind is that you’ll get a possibly confusing warning when doing this: if you check out a commit from its object name (a1b2c3) that will put you into a state known as “detached HEAD”, where HEAD, which usually represents your current branch, instead points directly to a particular commit. This isn’t something to worry about – it’s very useful for moving about in your history – but it does mean that if you create new commits when HEAD is detached, they won’t move a branch forward.
fork0 points out in the comment below the potentially useful shortcut git checkout -, which will checkout the previous branch or commit that HEAD pointed at.