At your back, in your face, violent cross winds...there is no exact science to judging, and there is no "best" way. But to score well, I think you need to have a method and be consistent with it. Here's what I've been using for a while:
1. When you see the wind gauge, imagine it's got the face of a clock behind it. Sometimes you have a 20mph wind with the arrow pointing straight at 12:00. Sometimes it's a direct cross wind pointing at either 3:00 or 9:00. Often it's somewhere in between. The first thing I do is determine how much wind is effecting the distance (head wind/tail wind) vs. effecting the direction (side to side). Say that 20mph wind is pointing at a 45-degree angle, or right between the 1:00 and 2:00 on a clock face. The way I judge it, you have 10 mph of wind at your back, and 10 mph of wind from left to right. Totaling 20 mph of wind effect.
To deal with the distance, I usually consider 10 mph of wind at your back will knock 5 yards off the distance to the pin. So if you're 150 yards out, you only need to hit it 145. **Keep in mind that that things like elevation changes, type of balls, if you use backspin are all things that might impact this** Also, I usually consider that for a short wedge, a 10 mph tailwind might only have a 3-4 yard effect, vs. a 3 or 4 iron might have a 6+ yard effect. This is where "feel" comes into play.
To deal with the direction, I assign a "value" to the aiming target box & little blue triangle under it. That is, if I have the box at/around the same distance to the pin, from the point of the triangle to the edge of the box is about 5mph worth of wind. So if I have 10mph worth of cross-wind from left to right, I first aim left of the flag until the right edge of the blue box is in line with the flag. That's 5 mph worth of wind. Now look where the LEFT edge of the blue box is, and aim further left until the blue triangle is pointing to where that LEFT edge was. Now you've just marked out 10mph worth of wind.
Here's a screen-shot from a St. Andrews hole:
Now a couple of things to consider:
For MY clubs/ball combination, I find that the edge of the box to the triangle when measuring wind effect is about:
5mph for wedges & short irons
6mph for mid to long irons
7-8 mph for woods/driver
The Burner 2.0 irons have a high launch, so that's what I've found works for them. Older irons I had I would figure 7-8mph value for the arrow to edge of box, just because they weren't in the air as long and weren't being pushed as much.
Also you need to consider elevation. If you are hitting your approach from 36' above the hole (like Oakmont #1), your ball is in the air a lot longer, so the wind will have a larger impact on the direction. Make sure you account for that.
Third, if you utilize a PUNCH shot, the ball isn't in the air as long, so for example on wedges that I punch, that 5mph measurement that I assign to the arrow/edge of box goes to 8mph.
So that's my method for playing the wind. I'm open to questions or suggestions, hopefully this helps some members trying to figure out the wind.
Oh, and last suggestion, make sure you hit the *ding* 
-pillsy (Tim)