As a homeowner you can remove it yourself. You only have to follow the rules and regulations set up for your juristiction. You can send it to the landfill in your own trash can or even take it to the dump yourself with no disclosure of material content.
If you contract it out, the contrator will have to charge you extra for worker protection, disposal costs, and removal permits for doing the same job.
As the homeowner, all you are really required is to simply keep the material wet. Keep it really wet. Your own level of protection is up to you. I would seriosly recommend, at least, a half face respirator and disposable clothing. Don't try to wash the clothes because it will never come out.
As a courtacy let your neighbors know what you are doing and that you are keeping it wet and why. It can save you a lot of headaches.
This information is for rigid tiles only (exterior siding, vinyl flooring, cement tile, etc..). If you have any questions you can e-mail me at email@example.com.