These are just some simple instructions for getting a bonded title in Texas. You want a bonded title if you bought a moped/motorcycle/whatever without a title, but don't want to go through the hassle of finding the title owner. This will also work if the bike has never been titled.
When you buy the moped, make sure you get a bill of sale. You don't need it for the bonded title, but you bond company will probably want it.
Once you have the bill of sale and VIN number recorded, go to your regional DMV office. Tell them you want a title an untitled vehicle, and they'll give you a pre-printed stack of paperwork to fill out. Fill out the paperwork and return it to them. They'll give you some new paperwork that indicates the bond amount and VIN history. The cost is $16.
Give a copy the bond amount paperwork and bill of sale to your insurance company. At this point, you'll also want to insure your moped (should be less than $70/yr). From your insurance company, get your insurance paperwork and surety bond. They have to mail a physical copy of the bond to you, so this can take some time. A surety bond of $500 cost me $100. The bond amount can depend on your credit history, since its essentially a bond against a fraudulent transaction.
Now, with the surety bond, DMV paperwork, and insurance, go to your local tax office. You'll pay sales tax (8.25%) plus a registration fee ($60 or so) and they'll give you plates and a title.
Finally, rejoice that you are no longer riding illegally.
(These are simplified instructions from this site)