You buy Tivos from Tivo, retailers (Amazon, BestBuy, etc.) or individuals. You either pay a monthly fee ($15) or lump sum for lifetime service ($250-$500 depending on promos). Works with all US cable companies, FIOS and DirecTV. Doesn't work with Dish or U-verse. Some companies do directly offer Tivo as an option, but not many.

Tivo has a great sale going on right now with half price lifetime service. I just bought a couple myself.

IMO, the main reasons to get Tivo are their superior interface (most cable DVR's interfaces look like my 1970s Atari), functionality (search integrates TV and all major streaming services which are all built in) and cost savings (pays for itself in about 18 months then is essentially free). Tivo also retains a high resale value. So if you ever sell, you get most of your money back.

The exception is DirecTV's version of Tivo. IMO, it's inferior to Genie. But if you prefer the Tivo interface, you'll probably like it better.