They are kind of like business cards, only larger (normally 5-1/2" x 8-1/2"). The front of the composite card is usually a model's headshot with her name typeset on the photo (or on a border of the photo), and the back has a series of photos featuring the model in different photographic styles. The back of the card also typically has the models stats (age, measurements, hair & eye colour, weight, height, clothing sizes, etc.) as well as the contact information for the agency the model is signed with.
If the model has particularly good features or special talents, that is also often listed on the composite card.
Most comp cards are black and white, however, many from larger agencies are in full colour. The actual style of the comp card can vary widely, so many agencies have a "stock design" that they recommend that models use. As with portfolio photos, models are responsible for paying for their own composite cards. Since you'll need a new set of comp cards each year, don't buy "in bulk" just to end up throwing away hundreds of unused cards. When you are starting out, 100-200 is a good number to order. You can always get more in the future if you run out.
If you are not with an agency, a professional photographer who shoots composites and portfolios can help in recommending photo selection, design, and a good local printer. There are also numerous companies who print up composite cards through "mail order." Make sure to request samples of their work before making an order, because quality levels vary drastically among suppliers.
Another possibility to is to make "photocopy-comps." A high quality colour photocopier (or a computer with a quality scanner and high-quality colour printer) can allow you to create some temporary composite cards until you are ready to have work professionally printed (for instance, if you need better photos, if you don't have money to print off a large batch, if you are waiting to get signed by an agency and want to use their format, etc.).
Composite cards are meant to be given out generously. Always keep some in your portfolio to hand out to clients, and make sure that you keep a ready supply with your agency so that they can send them out to prospects as well.
What Else Can I Try?
Have some photo business cards printed up (a miniature version of your comp card) which you can keep in a purse and hand out generously to any business contact you meet.
Get a web portfolio designed and keep it updated with current photos and information about your rates and how to book you for jobs.
Try to do collaborative projects with photographers to come up with postcards, greeting cards, posters, or calendars which promote both your talents. These might be sold or simply given away to prospective clients (one heck of a way to keep the client thinking about hiring you!).
Volunteer to do FREE modelling for local charities in their printed advertising campaigns. The more people see your face (for whatever cause or product) the more interest people will have in hiring you in the future.
Enter hometown beauty pageants and modelling contests. It's a great opportunity for you to tell the world (in your introductory speech) that you are a professional model working in the field of (...) in the community of (...)