First, corporate law is a broad category that covers
corporate governance (internal power structures between the Board, Executives/Officers, and Stakeholders),
mergers and acquisitions (exactly what the name implies)
, corporate finance (working with banks/lenders to secure funds for corporate operations, capital improvements, etc...),
securities (public offerings, SEC disclosures, compliance),
corporate tax (exactly what the name implies), and a variety of other subcategories.
I wouldn't worry too much about exactly what it is that corporate lawyers do on a daily basis; most 1Ls / many 2Ls don't even know. If you're really interested, go to any major firm's website and just scroll through their practice areas section. That will give you a good feel for what they do generally, but there's very little out there that will give you a feel for what they do daily. Much of it is due diligence (reviewing corporate documents), drafting letters, telephoning clients, making disclosures to regulatory bodies (if necessary), and working with companies on deals.
As for the second question, every major firm (Vault 100, NLJ 250) will have a strong corporate practice. For major firms, see generally
http://careers.abovethelaw.com/ and
http://www.chambers-associate.com/. Is there something specific you're looking for? These are good starting points but if something arises, repost or PM.
Disclosure: I worked as a 0L at a firm. I also was also confused about the various practice areas when I first started working, but you'll get used to the process and the structure. They won't expect you to know very much about how the firm operates and they will teach you on the job what they think you need to know. HTH.