I offer species-specific advice on each species page but here are some general tips.
Hire local guides
This is important. Hiring guides shows that you care about the primates. It builds relationships. You'll learn a lot, you'll make friends, and you will respect local communities. And, you're much more likely to see your species. I include my guides as contacts on species pages as much as I can.
Listen as much as you look
You'll often hear primates before you see them. Listen for crashing or leaves or warning calls.
Primates are often high and far away. You'll enjoy their beautiful coloration, varying textures, and endlessly amusing expressions much better if you can see them closely. Binoculars also let you keep a respectful distance meaning you'll stress the primates less and probably get to enjoy observing more natural behavior.
Be prepared to be out for awhile
Primates are captivating. You're likely to be out much longer than you expect. Bring a headlamp, lots of water and snacks, raingear, and good shoes. Prepare for inclement weather just in case.
Get a field guide
And online web resources on primates: