For the most part we don't "tie" it. Below is the process we use at the livery.
1.) Check the girth for any foreign objects; dirt clumps, sticks of hay, whatever.
2.) Take the cinch strap and insert it into the ring of the cinch. Loop it back around, through the rigging ring, and go through the cinch ring again.
3.) Now go through the rigging ring; only this time, taking the cinch strap to your left, looping it in front
of the loops you previously made, and back through the rigging ring from behind it. Now take it through the middle of the little "tie strap" you made.
You can see the same process in this video:
To be honest, this is obviously with a saddle. I personally know nothing of bareback "saddles."