That is actually one chord, called a slash chord (can you guess why?). All that means is that the lowest most note of the chord is going to be the letter listed after the slash, so in the case of D/F#, you would play a D chord as usual but you would add the fourth fret of the fourth string. This is also what is called a first inversion, because the first chord tone after the root is acting as the note in the lowest octave of the chord.