The wood from the Forestry is the only reason to have it. The wood will be automated to be put on a table to be made into furniture, or sent directly to exports. If it is sent to the table in the workshop, it could be made by a qualified prisoner into a Superior Bed. Wood sent to exports will be picked up by one of the delivery trucks and sold. Note that trees cost 100 each to plant and that full grown trees give 3-5 wood pieces (1 piece sells for 50$).

Tree -> Superior Bed:
Stages:
Sapling -> Tree -> 3 Logs -> 12 Planks -> 2 Superior Beds
Causes:
Bought -> Grow-> Cut -> Saw -> Carpenter Table
Cost/Profit:
-$100 -> -$100-> +$50 -> +$500 -> +$700
Note that the values shown above are for EVERY tree, except some logs may be sent to exports before they become beds, and that a workshop is required to make maximum profit.
So, the time a tree takes to grow is 5 days, and 1 tree will make $700 in those 5 days (not including the workshop time, but in theory, every wood and plank will be used eventually).

More Maths
If you have a 9x9 area of trees, 9^2 is 81, but each tree will take up 3x3 squares (3^2), which is 9, and 81/9 is 9, 9x700=6300, but over 5 days, so 6300/5, which simplifies to 1260.
So, with a 9x9 forestry and a workshop, you will make $1260 every day, UNLESS you dont have tax relief (See Tips and Tricks).

Sadly, the Forestry is not available at the start. As it usually is, The warden is needed, but so is the Foreman and the Gardener. Once grounds keeping has been researched, then the forestry will be unlocked. The Forestry has to be outside, if you couldn't read the room description, and requires gardeners to plant the trees and workers to cut them down. The forestry should be placed in a large area to maximize output.

A large problem I noticed while i was playing is that if you make a very large forestry, the trees would cost me way too much money. Make sure that you 1, have enough money to make a large forestry, or 2, make a small forestry first and gradually make it bigger. Otherwise, money becomes a big issue for a while. Trees cost $100 each.

Although the forestry is a useful room, it can also be very dangerous. The Forestry is home to contraband sources that are very powerful in the hands of a prisoner. The axe and the spade, the axe does more damage than a shank, but has no other special properties. The spade is a very useful digging tool and does a little damage. I have an "airlock" styled entrance with metal detectors on both doors, with a guard stationed in the "airlock". This security is only required if you plan on making a prison to go into the steam workshop, because actual players can choose to go into staff-only rooms, unlike regular inmates. Otherwise, the easiest way to stop these prisoners from stealing stuff is to make it a staff-only zone. This should stop almost all prisoners from getting any shady weaponry.

Instead of making the entire half of the map a forestry all at once, you can add a section of it each day. Doing this will spread out the growth of these trees and will stop a massive wood overflow on you workshop, which would reduce profits. This will also stop you from losing a ton of money right of the bat from buying too many trees.

During such overflows, an easy thing to do is sell planks or wood, you will lose profits, but it will stop the overflow after it happened.

There seems to be a bug with the cashflow, where values aren't shown properly...

Things I didn't know:
Trees grow faster on dirt than sand
"Selling wood log from the forestry before unlocking tax relief isn't a good idea since at the end you're selling each tree $150 - $45(30% tax) - $100(price of the sapling) = $5"