From StrategyWiki, the free strategy guide and walkthrough wiki

1. Don't hit the barbed wire.
2. Stay between the white markers.
3. You do not have to climb down, just walk off the edge.

[edit] When it doesn't work out

"When I get to the end of the course, time just runs out and I have to do the course over again."

You made a mistake somewhere in the course. The instructor doesn't always stop you or warn you immediately. However, he does let you know where you went wrong. Every time you complete an obstacle correctly, you get some sort of praise ("Good Job", "Hooah!", etc.), up until you miss an obstacle, then he stays silent. Run through the course again and notice when he stops giving you feedback -- that's where you messed up. The most common problems are on the fifth obstacle (the second high climb) and straying outside of the white posts. (There are a few spots where you have to jog a bit to one side or the other to stay on course.)

"I'm coming down the fifth obstacle, and the instructor says 'That's not the Army way' before I even reach bottom. I try climbing, jumping, nothing seems to help"

Typically this means that you crossed the obstacle improperly. To cross this obstacle:

1. Stay between the white posts at all times.
2. Go up and across the obstacle 3/4 of the way from the left edge, 1/4 of the way from the right. The key is that you are going across the cross beams, not along the long center or edge beams
3. When you reach the top, turn 180 degrees and walk backwards until you start to descend. When you reach bottom take a step or so backwards, then turn and proceed. While it's possible to just walk off this obstacle, I only completed the course once that way in many tries.
4. There's nothing tricky about crossing this obstacle; no jumping from beam to beam, or anything like that. Just go up and over in one smooth, straight line.