The numbers represent what fret of the guitar you put your fingers on. This is a D chord, but, at this point, that is not important. The zero on the D string means you strum the string, but don't put any of your fingers on the string. Don't be discouraged if all you get is some muffled notes and a buzzing coming from the frets, all of us guitarists start that way. It is all worth it when you learn how to play your favorite song and realize that it isn't as hard as it sounded like it was.
Chords can also be in arpeggio form.
That basically means that you pick each of the notes of the chord individually, rather than just strumming it. Now that you know how to read notes, there are a few more things to understand in order to get started. The 'h' between the numbers indicates a hammer-on . A hammer-on is when you play the note on one fret with your pointer finger, and put another finger on another fret past that one with another finger, without actually playing the note. This mutes the first note and makes the second one sound lighter than it would if you had played it.