Visit My Favorite WEB Search Engine and start 'clicking' your way throught the links that are listed to inquire about Asbestos Test Kits. Be SURE the kit you buy/get is rated for your particular 'situation'.
As an aside, I want to mention to you about what's known as Seller Disclosure. When you bought your house, or when you go to sell it, you MAY have to 'disclose' if there's asbestos in the home. Friable or not, check into this with your local Health Department. Encapsulation is the 'cheaper' alternative BUT if you have it professionally removed, you may have a 'better situation' when you do Disclosure when you go to sell your home. Heck, you may find that you DON'T have to 'tell' if you have encapsulated your asbestos-laden floor (assuming you have one.) But at the same time, you MAY be able to remove it yourself based on the Guidelines from your Health Dept.
As a further aside, the key to removing the floor is NOT to make the non-friable asbestos airborne. It becomes airborne when a hand or power saw is used or if there's a lot of 'friction' applied to the material during the removal process. IF you're 'allowed' to remove this type of floor yourself, I'd consider it. As 'bc' said, if you don't (for whatever reason), you'll be raising your floor by the thickness of the tile and backerboard, thus, creating other 'problems' when it comes to door heights, transitions into other rooms, and toe-kicks under cabinets.
If you have any more specific questions, post up! My best to ya and hope this helps.