You can try to prove it by cases (∨–Elim). The general form is:
If you have: ⊢ (A ∨ B), A ⊢ C, and B ⊢ C
Then you can conclude: (A ∨ B) ⊢ C
This means that if you've proved (A ∨ B) and you have proved (i) C from assumption A, and (ii) C from assumption B, then you have proved C from assumption (A ∨ B). This rule will give you the → direction.
To get the other direction, that is, from P to P ∨ (P ∧ Q), there is a rule (∨–Intro) to the effect that:
If you have: ⊢ A
Then you can conclude: ⊢ A ∨ B (for any sentence B)
Needless to say, if your system doesn't have those rules, then if it's complete (in the technical sense), then there must be some other set of rules or axioms that will allow you to prove the equivalence; your task in that case is to find those rules and apply them or find those axioms and instantiate them with the appropriate sentence letters.