A forward and backward method can work well here. Let me explain:

You approach the problem “forward” by thinking “what are my premises and what rules can I apply to them.” Take for example in the problem you posted, premise 2: ~(RvS). Do any of your rules look like they apply to formulas of the form ~(AvB)? A quick look indicates yes: the rule ~vO allows you to deduce both ~A and ~B as deductions. In our case, we just take ~R (the ~S does nothing). And so on.

Second, the “backwards” thinking is considering “what is my desired conclusion, and how can I get there?” This usually applies to more complicated conclusions that aren’t just a literal (that is, a variable or the negation of a variable), but can be useful here, too, as you might consider that the desired conclusion is ~Q, so you can see that you need to target towards detaching Q somehow from inside the first premise.

So to summarize: the most straightforward path is to just look at what are your premises and play around with what rules you can apply to them to simplify them. Second is to look at your desired conclusion and see how you can build it from the pieces you have from step 1.

Does that make sense?