Psalm 68 has been described by quite a few writers as the most difficult of the Psalms to interpret. One reason it is so difficult is because around 15 words are used only here in the OT.

It is a difficult psalm but when that is the case one thing we can focus on is what the Psalm teaches us about God. 
1. This Psalm teaches God as a warrior who conquers HIs foes- 68:1-2, 6, 12, 14, 17-18, 21-23, 28-31.

2. The Psalms shows God a compassionate and merciful God who cares for the weakest- 68:5-6, 10, 19-20.

3. The Psalm shows God as an awesome and holy God whose presence shakes the earth- 68:8, 15-18.