I think I can make it short and sweet for you.
You have two arms, the hitch arms, the left is pretty well fixed, the right (looking facing the back of the tractor) has a turnbuckle or a crank to adjust the height of the R arm.
You have a top link that attaches as the third point. This is also adjustable. Shorten the top link and you'll see the front of the attachment go down, lengthen it, and the front of the attachment will go up. Depending on what attachment you're using, more aggressive usually means shortening the top link.
Back to your implement, let the arms be just below the attachment pins as you can lift the arm onto the pin that way. Loosen the sway chains so that you have some play in the arms from side to side.
Hook up the left first, then the right. Adjust the R height if you need to to get it on. Put the pin through the sockets and pin and lock it in.
Hook up the top link and pin it. You may need to adjust the length to get it between the mounting bracket.
Once you're hooked up, on a level surface, look to see if the attachment is spaced evenly between the tires. If not, adjust the sway chains to make it so, and tighten them down, leaving just a little 1"-2" play (mowers usually should not have any play).
Look to see if the attachment is level on both ends. If not, adjust the turnbuckle/crank on the R hitch arm to make it level.
Adjust the top link so that you have it where you want the front to engage the ground, etc.
You don't want a lot of sway because the arms can hit the tires, and also, on a slope, the momentum of the attachment swinging could cause you to turn over.
If you have any other questions, we're here.
John