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How high you should tee up the golf ball really depends upon the club you are using for the shot that is required.
If you are using your driver, you want to work on teeing the golf ball up so that the top half of the ball is higher than the top of the driver club head. To achieve maximum distance with your driver, you want to hit the golf ball on the up swing. If you position the ball opposite your left big toe (for right handed golfers) and tee the ball up so that half of it is above the club head, you will be able to strike the ball on your up swing and strike it from the upper part of the club face. Striking from the upper part of the club face will result in the club face having slightly more loft added to it through impact and this will help you to get the golf ball launched high into the air. The higher you can launch the ball into the air, the more the ball will travel forward and as a result, the further you will strike the shot.
If you use the same tee height for your fairway woods, you will end up hitting the ball directly up into the air too vertically and the ball will finish only a few yards in front of the tee, as it will travel up too high and not forward enough. This is because the depth of the club face on your fairway woods is much shallower than it is on your driver. Using the same tee height as you would for your driver with a fairway wood will result in you being able to swing the shallower fairway wood club face directly under the golf ball on the high tee and this will result in the golf ball being struck from the top edge of the club face. Work on setting the tee height so that only the upper half of the golf ball is teed up above the club head and this will allow you to strike the golf ball from just above the middle of the club face and help you to launch the ball at an appropriate height to gain maximum shot distance.
If you are playing an iron shot or hybrid from the tee, then you need to set the tee height very low, only a few millimetres above the ground. You usually play your iron shots/hybrids from directly on the ground, so replicate this by teeing the ball low to the ground and this will allow you to strike the golf ball from the centre of the club face, which will result in a long, high, crisp golf shot.
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If you always tee the golf ball up really high, regardless of the club being used, you will hit some shots that fly too vertically into the air and as a result of this they do not fly forward enough and land only a few yards in front of the tee. Teeing the ball up really high will allow you to swing the club head under the golf ball and strike it off the very upper edge of the club face and this will produce a very high trajectory, but very low distance results.
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If you always tee the golf ball low regardless of the club that is being used, you may hit some very low shots that land early and as a result finish short of the target. Hitting your driver off a very low tee position will produce a shot that is struck from the lower part of the driver face. The driver already has the lowest amount of loft on the club face and striking from low down on the club face will de-loft it even more, producing a very low and short shot.
Sorry Try Again! - See Explanation Below
Tee height is crucial if you want to hit the longest shot that you are capable of. Teeing the ball up too high for the club being used will produce very high short shots. Teeing the ball too low for the golf club being used will produce very low short shots. To achieve maximum distance for the shot you are playing ensure you set the tee at the correct height for the golf club being used.