Ok, I've got the problem that my WE is in spanish, so I can't just post and image of the done trigger.
What you have to do is get the harvest ability (from a peon or a shredder, for example) and give it levels, each level with an increased speed (which is clearly shown) compared to the one before. If you don't want the unit to destroy the tree (just as Island Defense) set the damage to 0. After that, create an upgrade with the same number of levels as the ability you modified.
Then, create a trigger that every time you research the upgrade it increases the unit's ability by one, and so increasing the gathering speed. You can increase the amount of wood the units carry too, just change the stats in the ability.
I hope that helped, if you don't understand something, PM me and I'll try to explain better.