As a store administrator, you may choose to enable membership signup for users (See the "Allow customers to sign up for membership" setting in the section Store Setup > Cart & Checkout described here):
If membership signup is enabled, new and existing customers can sign up for membership levels they want. The account signup page and the customer account details page will provide the "Pending membership" field where it is possible to specify the membership level they require before submitting the form.
Once the form is submitted, a store admin can approve or decline the user's request for membership (See further below how to do it).
In the list of users (Users > Users list section of your store Admin area), users with a pending membership are marked as "requested for <membership level name>" (where instead of <membership level name>, you see the actual name of the membership level).
However, since a store tends to have lots of users, it's easier to find out whether any users in the store have signed up for memberships using the 'Search for users' feature on the same page (be sure to select the checkbox with the name of one or more pending memberships in the filter):
If you see a user with a pending membership request, you may want to check the user's profile and approve the membership request:
In the users' table, click on the user's email to access their profile information.
Scroll down the page to the Access information section of the user profile and locate the Membership field
Select the membership level requested by the user from the Membership field drop-down.
The membership level requested by the user displays as "Pending membership." The user's current membership level is shown in the Membership field. The "Ignore membership" option in the Membership field means that the user currently does not have a membership level assigned.
Click Update to save the changes.