Tri's vs quads is a topic for half a book. I recommend reading up on boxmodeling, face loops, and pole's. Get as much hands-on modeling experience as you can. It does get easier and easier in my humble oppinion.

Here's some quick examples when you should avoid tri's:
If you want to take the model into ZBrush.

If you plan to animate the character (tri's can be used but best be hidden in areas that does not deform and preferrably where it's not seen (inside nose, mouth, eye sockets)

Triangles can create uggly pole's on a mesh, but does not necessarily have to. Most game models are triangulated etc. This is another several chapters long topic.

If you are planning to convert the model into different formats, or go between nurbs,poly's, sub-divisions).
Again with reservation. Some convertions works just fine with tri's.


When to use tri's:
If it's a still image and it's not visible in the result, use as many tri's you want.

If the faces they make up are somewhat planar and does not deform at all.

If they are temporary geometry that you will later fix. There's no reason to keep a triangle that could be made into a quad, but they can be useful in the modeling process temporarily. Many prefer to kill the last 3-4 tri's at the end of the modeling stage when all geometry and loops are in place, and you have the flow that you want. Again if it's not easy to kill, hide it if you can.


Here's a way you can go from areas of higher resolution (more faces) to a lower resolution.