I drug the old tiller out of the barn this morning and took a few pics so hopefully you can compare this one with yours and help with understanding how it's supposed to work.
In this first picture, this would be in the transport mode, for moving it from storage to where you want to begin tilling. Wheels down, drag bar up:
In the next 2 pictures, you will see a close up of the drag bar and how it's mounted and what keeps it from folding back when in use:
In the next picture, I lowered the drag bar but left the wheels in place. The wheels are just barely off the ground:
Next shows the wheels removed, they slide in and out and are held in place with a pin and clip. I've also seen some that fold up out of the way:
And next is a picture of it ready to till with the wheels removed and the drag bar in the down position. Notice there are multiple holes in the drag bar so you can adjust the tilling depth:
And the last 2 pictures show the amount of play in the drag bar. This works well because if you need to pull it back a little bit you can without lifting, but the bar is pretty well vertical when tilling as shown in the last picture:
As Ray stated below, you push down on the handles to keep the tiller from going forward. Simply adjust the height of the drag bar to adjust how deep you wish to go. Bar deeper means tilling deeper. Ray also said he leaves the wheels down, but I disagree. Whenever the wheels touch the ground, that keeps the drag bar from engaging which means the tiller wants to pull forward and your still having to hang on to try to keep it from going forward. Let the machine do the work as it's designed to and you will be amazed at how easy it really is to use.
A couple of other suggestions, if your tines and worn and dull it helps to sharpen them as they will cut easier and lessen the bouncing. Also if your cutting new soil with grass, the grass bunches up around the cutting edges of the tines and that is like trying to drive nails with your forehead. Best to get rid of the grass first, or keep the tines clear of grass the best you can. Hope that helps, and enjoy your garden this year!