Psalm 73 is one of the most important psalms in the Psalter as it is placed at the beginning of book III. Here is the introduction from the ESV Study Bible. But note that the psalm should also be read in connection with Pss. 37 and 72.
This is a wisdom psalm, helping those who sing it to rest content even when unbelievers seem to get along without a care in the world, so that the faithful are tempted to join them. Their help comes from taking to heart where the different life paths of the faithful and the unbelievers are headed: each one is going toward either nearness to God or separation from him, a nearness or separation that will apply both now and in the afterlife. Psalm 73 is thus a companion to Psalm 49. The singer remembers that he discerned these different destinations while he was in the sanctuary of God, namely, at public worship (which points the congregation to what they should look for as they worship).
The following division (from McCann) is acceptable and useful:
There are multiple problems and questions that this psalm raises. Here are a few of them:
1) What is the psalmist's main problem?
2) How do you understand the 'turning point' in vv. 13-17.
3) What are some practical lessons that can be learned from this psalm when dealing with issues that question your basic beliefs about God?
4) How do you understand the 'entering in the sanctuary' in v. 17?
5) Reflect on vv. 23-28. What are the 'solutions' present in these verses?