Once you have identified the main clause, find the secondary clauses, and answer these two questions:
- What conjunction introduces the clause?
- What is the verb of the clause, and what is its tense and mood?
This should let you identify the kind of clause (e.g., purpose, protasis of a condition…)
You can then work out any complements to the verb, as you did for the main clause.
Once you have worked out the secondary clauses, you should look at attributive participles.