What does Psalm 25 teach us about God?
1. God is a God of forgiveness
25:6-7, 11, 18
God is a God of mercy- 25:6
Lovingkindness- 25:6, 7, 10
Good- 25:7-8
faithfulness or truth- 25:10
He forgives based on His goodness- 25:7- and His name's sake- 25:11

2. God is a God who teaches, instructs us in the right way
25:4-5, 8-10, 12-14
God instructs sinners in the way- Sin means to miss the mark- Judges 20:16- and those who miss the mark are taught the right way or right path by God- 25:4, 4, 8, 9, 12.
God is a God anxious to teach sinners and not just to judge them. 

3. God is worthy of our trust
25:1-2 We can trust in Him and lift up our soul to Him
25:15 He lifts our feet out of the net
25:3, 5, 21 Waiting upon Him is stressed in the psalm. In vs. 5 he waited on the LORD "all day long."
David has sins- 25:7, 11, 18- afflictions- 25:16, 18- troubles- 25:17, 18- and distresses- 25:17. 
God is worthy of trust in all these situations. 

Jesus in Psalm 25
25:19 HIs enemies were many and they were violent
25:8-9 Jesus taught the humble and afflicted- Matthew 11:25-27
25:16-17 Jesus on the cross was lonely, afflicted, and troubled
25:7, 11, 18 He forgives our sins via the cross- Acts 13:38-39
25:6-7 The thief asks Jesus to remember Him in Luke 23:42.
25:2-3, 20 God raised Jesus from the dead and did not allow Him to be put to shame