Excess smoke is a result of incomplete combustion. In other words the wood-fuel isn't burning efficiently. As Gary has said, this is often due to high moisture content, so always gather your wood dry and seasoned. Avoid collecting wood from the ground where conditions are cold and moist. Better to look for standing deadwood or deadwood caught up in high branches (but not too high! Ouch!). Also avoid woods such as willow which tend to smolder (but is great for a bow-drill set).
How you manage your fire is important as well. If you arrange your fuel as a tall 'stack' it will flame more and smoke less (and consume your fuel faster!). Conversely, if your burning fuel is flat and spread-out it will smoke a lot. Try experimenting with this and you'll be suprised how much effect this has.
Again it has to do with completeness of combustion. Watch carefully the next time a gust of wind blows your smoldering, smokey campfire into flame.
Hope this helps.