Sharing a workspace
Access is set per workspace: everyone who can open a workspace sees all of its tables. Choose what everyone in your organization can do there, then give individual members more access if they need it. Only the workspace's owner or an admin can change who has access.
Open the access settings
Open any table in the workspace, click Table settings (the gear at the right of the header) and choose Manage access. You can also open it from the workspace's menu on the Tables page.

Choose what everyone can do
Everyone in the organization sets the access every member gets. The workspace's owner is listed below it, and admins always have full access.

Pick one of:
Can edit workflow: columns, actions and table setup, plus everything below.
Can edit rows: edit rows, run actions and manage views.
Can view: open the tables, read-only.
No access: only you, admins and the members you invite. Everyone else loses access unless you invite them one by one.

Give one member more access
Under Invite specific members, pick a level next to the person's name. Not invited means only the setting for everyone applies to them.

To hand the workspace to someone else, click Change owner.
Common questions
Can I share one table and not the rest of the workspace?
No, access covers the whole workspace. Move the table into a workspace of its own and share that one.
What can someone with Can edit rows not do?
They cannot add, change or delete columns and actions, or change the table's setup. They can still edit rows, run actions and manage views.
Who can change these settings?
The workspace's owner and the organization's admins.