You are going to have a couple of different strategies depending on your site's architecture and the skill level of the developers looking at the issue.
If you are on VPS or dedicated hosting and have someone that can work on the code directly you'll want to install New Relic. It will profile your back-end performance live in production and tell you exactly where the slow spots are.
If you are on shared hosting then you're basically going to have to instrument your server-side code with timings to see if you can track down where the time is going manually.
Are you using a publishing platform of some kind or is it a custom app?
So I'm new to webpagetest and appreciate all the work that has gone into it. I have a couple of questions though...
The TTFB target - is that something WPT calculates? (e.g. it's not something I set myself)?
Also, I ran a couple of tests and I know our site has HUGE performance issues... in fact, ttfb was 5.594 seconds... But when I look at the target, there is no target. The line has no number next to the ms. I'm curious if that's due to our slow time or something else. As I present these scores, grades, and suggestions to our directors and CTO, I'd like to be able to give an explanation of certain metrics, and since I don't see a target TTFB, I'm not sure how to show them a comparison.
The TTFB Target is something that WPT calculates. It tries to set the target so that your server can spend 100ms doing the actual processing and you will still get an A and then it drops a letter grade for every 100ms after that.
It uses the socket connect time as a proxy for the RTT to the server and effectively allows for that much time + 100ms for the first byte after the request has been sent (the overall TTFB includes DNS and SSL negotiation which are also added in).
You can pretty much assume that anything over a second will fail given the letter-grade per 100ms fall-off. The target not showing up is probably a bug - if you can send me a ling to the result I can look into it.