We have some big news for you: God isn't the only divine being in the Bible. And Psalms makes that very clear. They have a pretty big job to do—asserting the dominance of God and all—that they don't have a ton of time to devote to the angels, but they don't forget about them.
So what do the angels do? In Psalms, they seem to protect the weak and serve God, doing his bidding. When God hears a plea for help, he sends an angel, who "encamps around those who fear him, and delivers" the Israelites (34:7). In Psalm 89, we get a more visual image of the whole shebang: God is depicted as sitting amongst a gathering of other holy, divine beings that serve him.
You might be thinking that this sounds a lot like polytheism, but it's not even worth speculating. Why? Because the ancients didn't think in those terms. That's our modern thought sneaking up on us.
If you were worried about the existence of angels, here's another doozy for you: God wasn't the only god back in the day. That's right. Many times in Psalms, the authors refer to God as the best of other gods. Huh?
Throughout the ancient world, other gods were all over the place. In Psalms, we're not at the point historically where the Biblical writers decide to declare God the only true god. Instead, they just let us know that he could kick the other gods' butts: he's described as "the God of gods" in Psalm 84:7 and again in Psalm 136:2. Because the Israelites are facing competition, asserting their own God's awesome-ness is essential to making their case to the masses.