You would go to the subsite and click, "people and groups". From there, click "site permissions". Both of these links are on the quick launch.
From site permissions, you would click actions and "Edit Permissions".
Then, give the users and groups the specific permissions you want them to have at that site.
I struggled with this back in the day and wrote about it here:
http://paulgalvin.spaces.live.com/blog/cns!1CC1EDB3DAA9B8AA!398.entry
--Paul Galvin, Arcovis
Microsoft MVP - SharePoint
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