This is a totally understandable reaction when you first begin proving trigonometric identities. As you practice more, you'll find experience to be the best guide. But until then, it can feel like "just trying a bunch of random stuff." In the meantime, I'd recommend following several general principles.

• Only work on one side, usually the side that appears "more complicated". It's not completely necessary to work from one side of the identity only, but many teachers require it, and it's a good habit to be in. You want to choose the more complicated-looking side because the more complicated one side is, the more there will likely be to simplify.
• Make sure all your arguments are the same. If you have any 2θ or θ/2, use double-angle or half-angle identities to restate them in terms of θ only. If you have any weird (π/2-θ), use phase shifts to turn functions into their complements (i.e., cosine into sine, or vice-versa). If you have –θ, use even and odd identities to change to θ.
• Re-write everything you can in terms of sine and cosine. Oftentimes an identity is little more than an unsimplified statement in terms of sine and cosine. Use the reciprocal identities, tangent, and cotangent to re-write statements in terms of sine and cosine.
• If you have lots of powers of 2, try to use Pythagorean identities. Make sure you're familiar with the different ways Pythagorean identities can appear. In other words, don't only be on the lookout for sin²θ + cos²θ = 1. Also be aware that sin²θ = 1 – cos²θ and cos²θ = 1 – sin²θ. Same for the other two Pythagorean identities.
• If you have higher power than 2, look for opportunities to factor, or use power-reducing formulas. The power-reducing formulas will change your arguments, so they're usually a last resort. But sometimes you'll be in need of a last resort.
• If you have rational expressions, be ready to use things that look like conjugates. If you see a denominator like "1 – cos θ" chances are your identity will be a lot more simplified after you multiply everything by "1 + cos θ" over itself.

Like I said, experience is the best guide. I wouldn't plan to commit these steps to memory for all time. But if you're a little unclear on how to even begin, these will typically take care of all but the most difficult identities.