I've perused through the manual and can't figure out how to use medical packs to regain health. There was an on-screen tip, that I missed, that I think explained how. (I feel dumb for asking.)
Shepard can fully restore his health by using Unity. In this iteration, it is a combination of Unity (From the previous two games) and the First Aid skill from Mass Effect the first.
Extra medi-gel now gives experience instead of credits, so there's no reason to be stingy.
The other big difference is that you do not have to use Unity to revive your squadmates - if you get to their position, you can revive them manually without expending medigel.
Finally, if Shepard has lost less than a full section of health, it will recover to full when his shields do, but this will never go beyond the current health pip.