If you ever need to manipulate a domain you didn't create programmatically, use the utility functions provided in odoo.osv.expression. The is_leaf, normalize_domain, AND, and OR functions will allow you to combine domains exactly the way that Odoo does. Don't do this yourself, because there are many corner cases that you have to take into account, and it's likely that you'll overlook one.

For the standard application of domains, see the Search views recipe.