Here's a better explanation:
DSL stands for Digital Subscriber Line. This is the physical medium used to connect your home to your telephone company. Think of DSL as a telephone line (literally). The telephone line connects your home to your telephone company.
With any line, you must pay for the service on the other end. Like the telephone, your line connects to the telephone company, but you can use (at least in most cities) whichever telephone company you wish, whether it be Verizon, SBC (or affiliate), or whoever.
The same holds true for DSL. Since DSL is a telephone line, you must pay for a provider. Some of the most common providers are local telephone companies. They tend to be cheaper in most areas.
So, if you wanted DSL access, you must first get a DSL provider (just as you do with dialup). I would recommend you try your local phone company first.