Informal Example
In this example, a small group of parents, who are most likely neighbors and friends, will come together to form an informal cooperative.  There will be little if any written rules or plan.  One family will call upon one of the other members of the cooperative to arrange babysitting on an as needed basis.  The plan will be decided upon on an individual basis.  No money will change hands and the parents' are on an honor system, agreeing to not take advantage of the other members of the cooperative by constantly using the co-op and never reciprocating.

Formal Example
A formal parent swap co-op would most likely be a group of parents who are large in number.  The cooperative could be formed from a group of neighbors that may or may not always be well acquainted with each other.  The rules of the co-op are written down and handed out to each family who desires to join the co-op.  There is also a list of phone numbers and addresses supplied to each family so that they can contact the other parents to arrange babysitting.  

Another formality would be "tickets" that are printed out and provided to each family in a predetermined number.  Each ticket would represent a specific time frame.  For example, if each family receives 8 tickets worth 30 minutes each, that would allow for 4 hours of sitting.  The parents who need the sitting services make arrangements with another family and then pays for those services in tickets.  The parents who just did the sitting now have their 8 tickets plus the number of tickets that they received in payment from the other parents.  With this method, no family would be able to take advantage of the co-op because if they are constantly using tickets and never replacing them by returning the favor, they will eventually run out of tickets.  The agreement to join the co-op is no tickets, no free sitting.   If one family needs sitting services in excess of the number of tickets they have, other arrangements would be made on an individual basis between both sets of parents concerning whether or not to subsidize tickets with cash.

Some items to consider when developing rules are: what the requirements for joining the co-op are; what the plan should be on location of sitting; rules of etiquette; how tickets are distributed and by whom; how tickets are exchanged and how they are collected once a member leaves the co-op.  Also, what happens if one family or a group of families end up with an unusually large amount of tickets with no plans to use them.  You may also want to develop a plan to have a president (rotating yearly or every 2 years) so that the same person is not always burdened with the responsibility of running the co-op.  This will also be important if the person starting the co-op finds their brood no longer in need of sitting services.  Oh, how they grow.

If the co-op is going to be extremely large, you may want to consider suggesting breaking it up into smaller groups, or you might want to charge a nominal one time fee to cover the cost of supplying the phone list, the rules and tickets.  If you are feeling adventurous, you could also plan for a newsletter to be distributed on a bi-monthly basis.

The possibilities are endless.  If you are interested in starting a parent swap co-op, get a group of parents together to brainstorm.  This is not only a great way to save a few bucks, it also will help you to get to know your neighbors better.