Buying brake levers, how do I find the correct ones for my bike? I took a hard spill the other day on my mountain bike and snapped my left hand brake lever in to pieces. 
The ones that snapped are stock alloy rubbish that came with a Specialized Hardrock 2010 Disc Brake model.   They are standard Bowden Cable brake wires with the little barrel shaped bit at the end that fits to the brakes.  (Do they have a name?)

I'm having some trouble purchasing levers and there doesn't seem to be much information on it online or much information on the products I'm finding.

To the point

What I need is Bowden Cable compatible brake levers but I have no idea how to search for them.  Sometimes descriptions will mention that they are for pneumatic, V-brakes, caliper or canti brakes but I've never seen anything saying that they would be compatible with my bike on any site. 

What am I doing wrong? Or what should I be searching for here?
Since it sounds like you have mechanical disc brakes (Avid BB5 or Tektro Novela not hydraulic) then any direct-pull or V-Brake lever should work fine with your cable. Searching for 'V-Brake levers' or 'mechanical disc brake levers' should provide plenty of responses.

For example, if you look at the spec page for the Avid FR-5 lever, you will see that they are compatible with both "Mechanical disc brakes, Linear-pull brakes." V-Brakes are a type of linear-pull brakes.

Note that most levers designed specifically for Cantilever Brakes will NOT be compatible. The key issue is that the levers must be direct or linear pull.  Some brake levers (e.g. Shimano's ST-EF60 shifter+brake lever combo) are switchable between canti's and V-brakes. If you don't set them to V-brake, you're not going to pull enough cable for proper braking.