How to identify and reduce first byte time

We have a custom ecommerce site that received an “A” for first time byte on the home page, but is getting an “F” on the pages that dynamically display content. I read through the documentation, but I’m having trouble identifying what to fix. How can I fix our site’s performance?

Test results
http://www.webpagetest.org/result/151124_BC_KYZ/1/details/

Site
http://bit.ly/1DVxfvh

One thing that’s puzzling is how long it takes for the drop-down, light blue arrows to appear in the top blue horizontal navigation. I’m trying to identify the bottleneck.

The standard ‘combine css and js’ to reduct the file count applies in general on the site, but that doesn’t affect TTFB.

Other than that I can’t really help as I only speak linux.