A decent boot fitter will look at many things, including, the shape of your foot (including instep), your posture and range of movement, the profile of your leg, your skiing experience, weight and strong/weak you are.
Many manufacturers have a unique fit, so don't expect to fit them all.
If you can go at the end of the day (once you've been on your feet all day) then it's generally better.
We used to also let you take the boot home (once you have bought it) to make sure the size definitely fits (it can be hard to assess in a shop). Make sure you don't wear it anywhere it could be scuffed etc. Don't sit down in the boots and don't wander around in them aimlessly. I always used to suggest doing something like the ironing! If they don't feel right at home then take them back and exchange for a more appropriate size. Don't get too OCD about wearing them at home though, it's a ski boot, not a slipper. You'd be amazed at how many people would bring boots back and say that they weren't comfy when wearing a home, then they'd mention that they tried them while sat down watching a movie for 2 hours. It's really just an opportunity to wear them without the pressure of being in the shop.
Once you are happy with them, have the inners heat moulded (if appropriate).
If you normally wear insoles then get some.
You need to communicate with your fitter and be completely honest. Seriously, this is the most important part. I'd often ask people about their skiing ability - men seem to always claim to be better than they are, and women often undersell their level of skill. You need a boot which is designed for the type of skiing you will be doing. If you tell the fitter that you will be skiing tough blacks all day then you will get a very different boot than if you said you were just starting to get to grips with easy reds. Some people seem to have a hard time admitting that they haven't much experience, presumably because they spend all day telling their colleagues what a great skiier they are
Also, avoid the busiest periods if you can. If you go on a Saturday afternoon you'll often have a fitter who only works part time and has 10 customers at once. Going midweek can often mean you get your fitter's 100% attention.