Preparing soy milk at home
It is basically as simple as you say (soak, blend, strain) ... just that you should also boil it (for long enough - cca. 10 minutes) to get rid of the fresh bean (grassy) flavor (mainly caused by oxidation of polyunsaturated oils in the beans), together with some other unpleasant side effects of eating uncooked beans (like the infamous gas-producing effect of some oligosaccharides).

McGee, On Food &amp; Cooking says:
The key to minimizing the development of beany flavor is to inactivate
the beans' enzymes quickly, before they have a chance to attack the
oils. This is done by soaking the beans to speed subsequent cooking,
and then immersing them in boiling water or pressure-cooking them.

There is a vast number of soy milk preparation instructions online ... this one has always worked really well for me: http://justhungry.com/milking-soy-bean-part-1-soy-milk with all steps and techniques described in detail, and you will also find some continuing posts on how to further turn it into tofu, if you wish so.
Depending on further processing steps and your personal preferences you might choose one recipe/preparation method over another, so I will not recommend any specifics, but in general this should set you on the right track.
p.s. I found that straining/squeezing through cheesecloth/cotton muslin/nut milk bag over a colander is a winning technique ... no need to go any fancier.