as Dovid said, a CLEC is an entire class of companies. CLEC is not a single company but rather a group of a few hundred at least.
The telecommunications act of 1996 required phone companies to open their systems to independent competitors who could sell local and long distance phone service to consumers. However the local phone wiring must be maintained by one company (otherwise it would be a disaster) so the ILECs (incumbent local exchange carriers, aka the baby bell phone company that services your area) maintain control but are required to sell access to the system to competitors at wholesale prices. The CLECs (competitive local exchange carriers) could then sell competing phone service to local residents, paying the ILEC only for the physical line itself.
This worked decently well however CLECs have now moved to provide something far more useful to us- VoIP access to the PSTN. Because they already have their PSTN links, they can accept VoIP calls and send them to real telephones. There are a small handful of large CLECs like XO, Level(3), global crossing, etc that have a lot of PSTN links and sell huge numbers of minutes to VoIP reseller providers like Vonage etc.
Generally a CLEC won’t want to deal directly with you unless you plan on pushing a relatively large volume of calls, 100k-1million minutes/month minimum. In other words, service providers only. However you can buy service from a reseller and pay very reasonable costs that way.
There are two types of resellers- ones that sell ‘voip lines’ and wholesale providers.
Wholesale providers (ie- connect.voicepulse.com) sell you the pieces and you pay as you use them. You can get a DID (phone number) either for a flat monthly fee of around $10-15 or some sell DIDs for $2-3 with a per-minute fee. You also pay for outgoing minutes on a per-minute fee. With a wholesale provider, you pay for only waht you use. You can also set your own callerID number for outgoing thru a wholesale provider. These providers usually lack features like voicemail, forwarding, etc as you are expected to provide this yourself.
Other providers sell ‘voip lines’. This is where you pay a flat monthly fee (usually around $20-30) for unlimited calling in the US/canada and a few other places. You can’t set your caller id but it does include unlimited in/out usage and features like voicemail. examples: viatalk.com, quantumvoice.com.
voip-info.org may also have more useful info
and also the providers i suggested are good ones, give them a shot