How to relate to 2 taxonomy with category

http://codex.wordpress.org/Class_Reference/WP_Query#Taxonomy_Parameters

I recently dealt with a similar, although much more complex problem where I had to guess taxonomy names that had no naming convention. I built a whole bunch of abstracted functionality to automatically build my queries for me – your need is simpler though, you might as well do these as the link above explains.

The thing to keep in mind is that there are many nested arrays in this situation. That can be the big gotcha in all this – the arrays can get confusing.

$query = array ( //array level  1
     'tax_query' = array( //array level 2
             'relation' => 'AND' // actually in array level 2!
              array( //array level 3
                  'taxonomy' => 'some_tax',
                  'field' => 'slug', // 'slug' or 'id'
                  'operator' => 'IN', // 'IN', 'NOT' 'IN', or 'AND'
                  'terms' => array ( 'some_terms', 'some_terms2' ) // array level 4
              ),//<--comma!

             array( //array level 3
                  'taxonomy' => 'some_other_tax',
                   'field' => 'slug', // 'slug' or 'id'
                  'operator' => 'IN', // 'IN', 'NOT' 'IN', or 'AND'
                  'terms' => 'single_term' // no need for array if only a single term.
              )
      )
);

Another important thing to look into is the distinction between ‘relation’ and ‘operator’

EDIT: Modified to ‘terms’ values to show that it does not need to be an array if you dont want to pass multiple terms. Also, when you do pass as an array, you can pass any number of terms you want.