How to use a relational database to store all users who belong to a group, and all groups which a user belongs to?

Question

This is a beginner question:

A user can belong to many groups, and a group can contain many users.

Let's say the two tables look something like this:

user_id user_name user_email

group_id group_title group_description

Where and how do I store all of the users which belong to a group and all the groups a user belongs to?

I can't imagine the groups table having a users field which contains comma separated user IDs being an acceptable solution. I think I get the basic concept of relational databases, but I'm not sure of the implementation. I get the one-to-one relationship, but I'm struggling with one-to-many. Is what I'm dealing with in this example two separate one-to-many relationships?