Membership Pro uses jQuery Validation Engine for client side validation. If you setup Validation Rules for a field, as soon as you enter data for that field, the engine will validate the data you entered with the configured rules and if it's not valid, an error message will be shown to let you know about the error and correct it.
If you want to validate data of a custom field using this custom field, go to Events Booking -> Custom Fields, click on a custom field to edit, enter the rules you want to use into Validation Rules setting of that custom field. For example:
See http://posabsolute.github.io/jQuery-Validation-Engine/#validators for list of validators supported by this library and use the one meets your need
To help you configure it easier, the system tries to populate Validation Rules automatically base on two settings in custom fields: