There are a couple of ways to change a user's role on a site.
When dealing with multiple sites/users, an Administrator can do this from the Subscription screen:
Then select Users and Site Allocation:- 
From here, selecting Users will allow you to allocate sites by user:
Whereas selecting Sites will allow you to allocate users by site:
Dragging and dropping either a site or user to the middle column will allow you to edit the users role on that site:
For individual sites, select Site Settings from the specific site's dashboard:
Select the user from the right, under people, then select Change Role and Save:
For a break down of site roles, please see this article: What site role should I have?