How do I connect the ground wires to the new light fixture?
You made your life a lot easier by keeping your nose out of the junction box, and not messing with that rather important bundle in the back that rather importantly needs to be not messed with (for a skilled person that is the Rosetta Stone for what's happening in this box.) 

Grounds

In electrical, grounds are the easiest.  Their color-codes actually mean something and all grounds go together always.  Ground color codes are Green, Yellow-Green, or Bare, and are standardized worldwide except the former Soviet Bloc.  It's also two-way -- those colors are always ground and ground is always those colors.

All those ground wires should be spliced with any grounds from the lamp.   Use a red or tan (i.e. large) wire nut. 

I also see a green screw on the fan junction box; get about 9" of bare #12 ground wire from a local hardware store (one that sells it by the foot) and wrap one end around the screw (clockwise) then tighten.  Add that wire to the aforementioned bundle of grounds.  

Neutral is not ground.  This "grounds always together/always that color" does not apply to neutrals. Sometimes separate groups of neutral must remain separated, and white wires aren't always neutral. 

Rest of the wires

The two groups of wires dangling down are the ones you want to hook your new light to.   

The light's black wire(s) go to the solo black.  A yellow wire nut will be perfect.

The light's white wire(s) go to the two white wires, which must also stay together.  A yellow wire-nut will be fine unless there are several bulky wires from the fixture, in which case use a red/tan.