Yeah I think you've got it. I took some photos which I hope will make things clearer (assuming you're right handed).
This is for the D chord.

Start by putting your 2nd finger on the 1st string (thinnest) - 2nd fret.

Then place your 3rd finger on the 2nd string - 3rd fret.

Finally place your 1st finger on the 3rd sting - 2nd fret.

My hand is at a bit of an angle there. That partly because I'm trying to photograph it and partly because that's how I usually play. Try to have your hand more straight on.
Pluck stings 1, 2, 3, and 4 leaving out 5 and 6 (the lowest two). After you understand the concept of the chord diagram for D Major learning the other chords should be much easier.
It'll take some work to get the too all ring out properly often you'll find that your fingers are touching string they are not supposed to and muting the sound.
I actually learned the E Minor and A Major chords first because I personally found them the easiest. If you want you can try learning these first as a little stepping stone to D.