To configure who can access a table click on the "More..." button and select the "Permissions" menu item:
Permission levels
Any table has three permission levels and you can assign any user to one or multiple levels:
"View and edit records, change table structure"- users will get full access to the table. He can manage table's structure and work with data.
"Add and update records" - limited access. User (or group) can work with data but table structure cannot be changed.
"View table records" - user can see the data, but updates are not allowed to this user or group.
You do not need to add user to all three levels to give full access - only add them to level (1) as it includes all the permissions from levels (2) and (3). Same way, level (2) already includes all permissions of level (3).
You can use groups to grant same level of access to multiple users. You can even user "All Users" group to grant access to all users.