Veteran difficulty is harder then CoD4 but easier (in some places) then CoD2. The first few levels (Semper Fi, Little Resistance, etc) are easy, but the last couple of extremely difficult. As a general 'Veteran surviving' guide, follow:
1. Patience is a virtue. But don't be to patient! Never enter a battle unless you have other soldiers with you. They will make your life a lot easier. Some places have enemies that infinitely spawn, so here you will have the move up to stop the influx of enemy soldiers. Others, you just need to kill every soldier. These are the ones you need to be patient on. Make sure every last soldier is dead before moving on.
2. CoD: World at War has been referred to as CoD: Grenades at War. True, true... It is literally raining with grenades on Veteran, as if the German/Japanese soldiers have the Catch skull on from Halo 3. If you see the 'RB to throw back' signal come up on your screen, PRESS IT! Grenades take a while to detonate in the campaign.
3. Smoke grenades, although having no lethal capabilites, will make life a lot easier. Especially with MG nests. You start with 4, with ample amounts of them around you. Don't spam them however, only use them against heavily fortified positions where you can flank them or against MG turrets.
4. Being prone and crouching is a very big part of running this game on Veteran. Chances are, most of the cover you find will be smaller then your standing height. So go prone/crouch. This will make you a smaller target, thus harder the hit, and in turn you have less deaths.
5. Treat Veteran difficulty like Realistic in Rainbow Six. Cover! Cover! Stay in cover at all times. Make sure this is cover like cement walls or rocks, because enemies can still shoot through flimsy wooden walls (It's the Call of Duty 4 engine, remember?). And remember, if you want to help out your teammates, peak out on the side while prone or over the top and shoot a single burst on a single guy. Go back down and reload, then rinse and repeat.