Lead with big names (if you have them) but the basic formula is -
Company(X) had Problem(Y) that was solved by using (Z)
Bullet-point the lead, then a paragraph outlining/expanding what was solved by using (Z). Whenever possible use facts and figures in this opening paragraph.
Always check with existing customers whether or not they would be ok with using their name or other easily identifying information in the case study. Most are ok with it, some have policies about vendor/supplier endorsements so check first (and run the final draft past them to make sure they are happy with what you have written).
As gus_massa said - Take a look at other case study examples to get a feel of what ever format has the most 'punch' to you and copy/steal the format.