how do I add a table and where clause to query object using hook_views_query_alter()?
I don't know enough about your problem to say whether using  hook_views_query_alter is the best approach.

In regards to the error you're getting, the answer is in the error message: the query object you have is an instance of SelectQuery. If you look at the documentation for SelectQuery you will see that it doesn't have an add_table method.

Instead you should use SelectQuery::addJoin (or one of the more specific methods, such as SelectQuery::innerJoin, SelectQuery::leftJoin, etc.)