It's a process of filtering and negotiation. The CD's job is more business than creative.
The casting director starts the season off by meeting hundreds of models during precasting. Each agency will send her their girls and within a few a mixture of new and old faces herd through the CD's office. Often top models will skip precasting altogether because the CD doesn't need any convincing to hire them.
During precasting, the model hands her compcard to the CD and walks for her. Typically the CD makes some notes for herself on the back of the model's card. Then an assistant takes photos of the model that are uploaded onto the CD's database. At the end of the day, the CD will sort through all the cards into piles, often YES, NO and MAYBE and possibly according to which shows she is casting. Some CDs are old school and keep their cards in binders divided by agency and show. They may flag girls for certain shows within those binders.
After precasting is over, the CD moves her office to the house of the first designer whose show she is casting. There she reaches out to agents to send in a number of models she saw during precasting (or didn't see if they're top girls). This number varies with the show but I'd say ranges from 50 to 150. The process is the same as during precasting except that the stylist (and possibly designer if it a smaller company) is sometimes present, models' digitals are printed out and stapled to their cards, and occasionally the dressers will try looks on chosen models. As casting goes on, a board is created of top picks with models' cards/digitals. The CD creates this board based on which models she thinks the stylist and designer will like best. Who has more more clouds, the designer or stylist, depends on the show. I've seen it go both ways, but typically the stylist's word is god. The stylist/designer and CD look over the board together and the CD adds to and subtracts from the board based on her client's wishes. At this point the stylist/designer will typically communication their vision for the show to the CD, "I'd like more fresh faces this season. These girls are looking too old."
After this meeting, the CD and her assistants reach out to the agents of the chosen models to check their options and negotiate rates. (That rate depends on the status of the model. A newbie typically gets about a grand to walk a show -- her agent receiving a 20% cut, while an established major model like Julia Nobis makes about 10 grand per show.) If the CD is given first option on a girl, they will put a colored dot on her card and schedule her for a fit or a fit to confirm. If they are given a second option, that means another designer has a first on her and the CD will have to wait or negotiate with that model's agent to see if they can turn it into a first. This is where things can get ugly and messy, as shows conflict with each other and fighting about options is common between agents and CDs. It is advantageous for a CD to have strong relationships with agencies because they are more likely to do her favors, like give her a top girl for a smaller show.
During fittings, the models who have made it this far will come in to try the clothes on. Sometimes if they are a poor fit, they will be pulled out of the show and another model will take their place.
Hope that answers your question.