How can I create many to many relationship between the objects in Salesforce?

You can create many-to-many relationship between two objects using the Junction Object..

1. Your first object (master )     ======>  Junction object (child)
2. Your second  object (master) ========> Junction object(child)

You can to create a custom object and add 2 master-detail relationship in it.

Example of many-to-many relationship include :

Products and Price Book objects which are connected via Price Book Entry (Junction object)