Just like the previous games from this series, Farming Simulator 19 also gives you the option to cut down and sell trees. A good way of doing that is to sow them and collect on your fields. You can also cut down trees that grow on your parcel. At the beginning of the game, you probably won't be interested in getting money by cutting trees - you will only want to get rid of them to have more space. The easiest way to do that is to go to the Shop and buy a chainsaw for $1,000.
A tree that was cut down leaves a tree stumps which still is a hindrance. To remove it, buy FIS ST 65 T (this machine is in the Forestry equipment category). You can attach this machine to any of your tractors - the machinery cuts tree stumps and removes them.
Bushes are different. They are plentiful and can cause you a lot of problems during the game. To remove them, you need to buy a plow (you can't use a cultivator / harrow nor subsoilers). A plow has the option to create new fields - this also removes any bushes. Use a plow in the place with bushes and get rid of them.
Plowed parts of your field must be driven over with Meadow Roller Vario (Miscellaneous category in the shop). Deploy the roller and attach your tractor to its side. Go over your field to revert it back to a ground with grass.