Crawl everywhere. It'll help you blend in more.
Always change your camo and face paint to best match the current terrain.
Lean against trees and stumps. Put on the right camo, and guards will usually walk right past you.
Use First-Person view to look ahead. Use it a lot.
Proceed slowly. This is a sneaking mission after all.
Most important of all: use your three "radar" devices, and use them wisely. The original game was balanced around them. The motion detector shows organisms that are moving, but not those that are standing still. The sonar shows the position of everything when you let out a pulse, but it can be noisy and alert nearby enemies to your presence. And the Anti-Personnel Sensor (APS) can inform you how close hostiles are, but you'll have to rely entirely on the vibrations to do so.