There are a lot of ways to do this from a WordPress perspective. It depends on:
- Whether or not you want the products displayed on the dashboard of each of the subsites
- whether or not you want to have them show up in search results on each site
- Whether or not you want to associate them with the same categories on each subsite
- How you implement products in the first place in your default site
- How you want to format the products on each site
- Your level of programming expertise
- The amount of time you have in which to finish your project
For example, there are plugins that will help you create a post in one site, and then copy them over to another (so there are multiple versions of each post), as well as plugins that will help you pull posts from one site and display them in another (but there's only one version of the post).
You can also write your own code to do this, getting exactly what you want, but this is more advanced.
It all depends on how you want to administer and display the products.