Invite people to your workspace by selecting the appropriate workspace from All Workspaces View then placing your mouse to the right of the workspace name. Hovering your mouse next to the workspace name will display a Pencil icon. Clicking the Pencil icon will give you an option to Invite and Manage members.

If your account does not yet have All Workspaces View, you can use the gear menu at the bottom of the workspace section in the left pane to access the Invite and Manage Members dialog.

You can choose to invite the person as a full member of the workspace or as a Guest. 

 

You can also invite people to your workspace from the assignee or follower field in the right pane of a selected task. Just type the person's name and click the invite option.

There's also the "Share Asana" button that gives a few different invite and share options.

Remember that once invited, new users will have access to all shared projects in the workspace unless they are invited as Guests. Learn more about Guest Accounts here.