There's lots of ways to do it! No single way is necessarily the right way. Your progression certainly works, and you're right that preceding the Am chord with its dominant (either an E or an E7) is the best way to strengthen the effect of Am being the new home key. You can actually follow the E (or E7) chord with either an A minor (A, C, E) or an A major (A, C#, E) depending on which key you want to go to.
Rhythmically, another thing that can help to strengthen the effect of the modulation is to place the resolution to A minor (or A major) at beginning of the following phrase. So, for example, if your phrases are four bars long (with one chord to a bar), then end the fourth bar with the E chord, and then the next phrase can start in the new key of A minor (or A major if you'd rather). Then your progression might look like:
C _ _ E7 Am ...
where the two "_"s can be filled in by pretty much anything. I've tried various combinations of F, G, C, Am and Dm, and they all seem to work pretty well. In fact, I haven't found a combination yet that doesn't work. Play around with it.
I would consider preceding the E7 with something other than an Em, though, just for the sake of variety. Unless it's the specific sound you want, pretty much any other chord will add something more to the progression.