The first of them is D major. For this chord, you only need to strum the first four strings, leaving untouched the two lowest ones (A and E).
In this case, your first finger will be in the second fret of the third string, your second finger will also be in the second fret but this time in the first string, and your third finger will press the third fret of the second string.
What a mess!!!
Well, yes, you will have a lot of fingers in a small space, but I can assure you that describing (and reading) the chord shape is more difficult than playing it!
Trust me and try it. It isn't really difficult, and it has a really nice sound.
You should be aware, again, of pressing every string with the proper finger and of not touching any other string with this finger, or you will end up muting it.
After preparing the position, you should check that all four strings sound when you strum them and that the chord sounds right.
This is a very common chord and it will open you up the possibility of playing many new songs, so do not hesitate spending some time practicing it. Also, try to do some transitions, for instance from and to the Am, C or G chords.
Some of the new songs you can use to practice D are: