Remind your group that various different writers composed the Psalms. Both the common man and king penned the Psalms in the beautiful form of poetry. They were written with a range of emotions that we all feel from time to time. They were not composed by theologians but by individuals trying to figure out life and who God is. The Psalms are wonderful ways to express to God what we are feeling at times of worship. We may be angry. We may be questioning why something is happening. We may be thrilled by God's moving in our lives. Whatever emotion, whatever we are going through can be expressed through the Psalms.
You may do this worship idea one of two ways:
Give your group about 5 minutes to choose one of their favorite Psalms to read for worship. Tell them they don't have to read the whole passage but perhaps just a few verses. They don't need to explain their choice, just take turns reading their selection. Assure them that even if they choose the same Psalm as someone else it is still appropriate to share theirs.
If your group will have a difficult time doing the above, assign one of the following passages to several different group members. Have them take turns reading their Psalm.