READING CHORDS

What does it mean when there are two chords listed and how do i play it?

I.e D/F#

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.

same thing apply to chords writtend as CaddD ?

No. CaddD would mean play a C major triad (C, E, G) but add the note 'D' to the chord. That would also be the same as Cadd9 (D is the 9th ). D/F#, I always took that to mean that you play a D major triad (D, F#, A) making sure that the F# is the base note of the chord.

Now, I've also seen a much more complicated explanation of this type of chord form in a book called "Chord Chemistry" by Ted Greene. According to that book, D/F# could be Dmaj7 or Dmaj7#5. I just think that is way to complicated and quite frankly I have no idea if that book is right or wrong.

After a while, you come to understand that chord progression are pretty much based on one note changes, 90% of the time... Thinking in those terms let you understand why you go from one chord to another.
Let's say it's easier to say that you go from C to C/B down to A minor(understanding the bass movement) than saying C, Cmaj7, A minor... Well, anyway, that's what I use...