If you want to cut trees you will need a big initial budget. This is because there is only one machine that allows you to cut trees and it costs more than 300 000$. In addition to that you also need Fliegl Timber Runner trailer that allows you to transport logs + compact front end loader and a log fork attachment (or a loading vehicle with Ponse Buffalo trailer).
Get near a tree - not all of them can be cut, some of them are only textures (you can go through them - those trees can't be cut). You must adjust your position slowly - move the arm closer to a tree, then you must stop and press the action button - this starts the cutting, cleaning a tree and cutting it into pieces. Then, load logs on a trailer and take them to one of the three points of sell.
You can use a milling machine to remove tree trunks that are created after cutting. A new tree will grow from that place after about an hour. If you won't remove a trunk - a tree won't grow and because of that you can leave trunks in places where trees are a hindrance to you (e.g. near your fields). Tree cutting is quick and profitable - one tree gives you 3 pieces and one piece is worth about 1500$.