Every agency is a bit different but normally the whole process takes about 60 seconds if there are a lot of people there. You walk in, are seen by an agent who will immediately tell you if you are model material or not. If they think you have potential they will ask to see your pictures (not professional photos, they just want to see snapshots to see how photogenic you are). If they like your look they may ask to see you walk, measure you and take a few photos then ask for your contact details. If you are not at all model material they will tell you upfront you aren't model material and won't bother photographing you.
At 14 don't be surprised if you are rejected - it doesn't mean you aren't model material but you might still have very young features. An agency isnt' going to sign a 14 year old unless she can pass for 18. You can't send a girl down the runway for Prada if she looks like a little girl playing dress up. If you look at any runway show, many of those models are only 15 or 16 but they look much older. So if your features have not matured yet they may tell you that you look very young and to come back in a year
