Tuned GDAD here are some chords which will get you going (the numbers refer to the fret, going from low G to high D)

D maj/min (because it has no third in it)

2,0,0,0

G

0,0,2,0 or 0,4,2,0 for a minor play 0,0,1,0 or 0,4,1,0

A maj/min (no third)

2,2,0,2

C (I guess this should really be C 2nd or C add 9)

0,2,3,0

A proper C would be 0,2,3,2

Bm

4,4,2,0

Em (I guess the top D shouldn't really be played, but sounds fine)

7,7,5,0

Once you have got this under your belt, start looking for some alternatives. Now many of these chords will not be pure (a C for example shouldn't have a D in it - but it still sounds fine) or be ambiguous with respect to major or minor because of the absence of a third, but the nature of the sound is just right for folk music.

D

7,7,0,0

C

5,5,0,0

G

0,5,5,0

Here is a nice ascending run to try

2,0,0,0 - 4,5,0,0 - 6,5,7,0 - 7,7,0.0

Another A

6,7,7,7

Now here's something nice about the bouzouki. When playing the most basic D or G down near the nut, you have lots of fingers left over to put in little fills of melody, or to let strings ring between chords and then fill in with some melody.

What is theory should sound dischordant will often have a very nice rich sound to it. Go on, throw some caution to the wind!