I've been going through the table of contents but I don't see anything about running adventures or campaigns on Airships or anything about combat on airships. 

Is there anything in the sourcebook about that or anywhere that I could get that information? I had the sourcebook in my cart and was ready to buy it until I thought that, maybe, I should check first.

There are no official rules for airships in any official published book. The closest you get is the airship vehicle stat block in the 'Of Ships and the Sea' Unearthed Arcana article that was eventually released in part within Ghost of Saltmarsh

It may not be quite what you're looking for, but the acquisitions incorporated book contains stats for their 'battle balloon'.