SharePoint Monitor

If you don’t want to add a user to a SharePoint group but want to give the user a specific set of permissions unrelated to a specific group then navigate to the site’s security page (Site Actions > Site Settings > People and Groups > All People (located on the left navigation bar).
This page lists [...]

To add or remove users from  a Group firstly navigate to the relevant group (Site Actions >  Site Settings > People and Groups > yourGroup ). Then in the group page, click the New dropdown and select Add Users:

This opens the Add Users page (below) where you can either add users by entering them [...]

To add a new user in SharePoint (MOSS or WSS) the first step is to create the user on the server. Normally Sharepoint users are created in the Active Directory and then given permissions to use the Sharepoint installation.
Creating a User on the Server

Go to Start > Administrative Tools > Computer Management to open [...]