How do i get the sawmill or any of the woodworks to actually produce Lumber? Cant figure this out.I build them and tell them to produce lumber and they immediately go to the arrow under the line icon. they never seem to produce anything. HELP PLEASE!!!!!!

The Arrow under line icon means that you've got resource limits set. The limits don't tend to apply to 1 resource so much as a range of resources such as food, or in this case "building materials". You might have a load of another type of building material maxing out your resource limit while not having any lumber. The resource limit is usually displayed in the building that produces the good, in the short term you could just increase that, but overall you'll be wanting to find out what you've got maxing out that resource, and normalise your stock levels.

Hello,
With the forestry building it can take a while until you see the first lumber, especially if the area they are working in does not have a lot of trees.

The forestry building once built comes with both planting and harvesting both already active. If you clicked on harvest thinking that activated it then you actually deactivated it.

Also, there are no buildings called "sawmill" or "woodworks" (or a resource called "lumber", technically :P ) in the game itself. I'm guessing the OP's using a mod or modpack.

The woodcutter worker in the woodcutter building uses logs to make firewood. Firewood is governed by the fuel limit. This starts at 200. On a medium start, we already have 200 firewood in the stockpile so no more will be produced until somebody takes some home for a private store ready to heat their house. This will not happen until we complete a house.

In the basic game, woodcutters compete for logs with builders, who use them directly. Logs come from cutting down trees. Foresters do this only if the reserve of logs in the stockpile is less than the log limit (which is the first one on the list). Laborers told to harvest trees (or who have to do so incidentally in preparing a building site) produce logs regardless of the limit.

PS:
After completing a woodcutter building, remember to assign somebody to the woodcutter job! (To be pedantic, tell the work manager that one person is needed - we have no direct control over who it will be.) There is a different warning symbol for a workplace without a worker, and another for one lacking its raw materials.

Oh, and when the WORK button on the display we get by clicking on a building is lit up, this means the building IS meant to be working (everything else permitting) so clicking it means "DO NOT WORK". When the button is faded out, that is when clicking it means to start work.

Pretty sure the OP is referring to the Colonial Charter mod. In that you can get a Sawmill, and that will produce "Lumber" from logs. Unfortunately the resource limits in that mod apply cross material as there are too many materials for individual limits.