Initial assessment
On arrival, the bike fitter, Paul Smith, took me and my bike to the first-floor bike fitting studio, and set the bike up in a turbo-trainer. I had already provided the make and model of the bike, and Paul had downloaded the basic geometry into his spreadsheet. 
He then recorded all the specific details of my current setup: saddle height and set-back, bar height, reach. We then discussed my objectives for the fitting, and he did some measurements of me and some exercises to establish my range of motion and flexibility. 
Even before getting on the bike, the exercises had shown that my cleat position was not right (too far back and toes-in rather than toes-out), so Paul fixed that. We also checked the width of my sit-bones (thankfully a hands-free procedure) and the height of my foot arches in case insoles might be beneficial (spoiler alert: they were).

Main fitting session
It was then onto the bike to do some spinning at various speeds and loads while Paul looked for problems with my position. The main issue was that my saddle was too low and too far forward. We tried a few different positions to reach an optimum nearly 40mm higher than baseline, and with the seat a few mm further back on its rails. At the front, I was immediately getting lower on the hoods due to the higher seat setting - maybe too low, so we moved one spacer below the stem to raise the bars about 5mm. 

Another consequence of a higher seat is that you put more weight on it, and my original seat was on the narrow side for my backside. While I had got away with it with a lower seat position, it was less than comfy at the optimum height, so we changed to a slightly wider seat, which was much better. 

At this point we also tried riding with and without insoles to fit my arch shape. The difference is subtle, but feels worth it as my feet feel much more connected with the right insoles in place.