Dual taxonomy term query into a custom post

We would like to use two custom taxonomies together with custom posts. We would like to be able to call the specific term into the custom post without calling the entire taxonomy.

Example:

Custom Taxonomy 1 — Colors:

Blue
Orange
Red
Green

Custom Taxonomy 2 — Party Favors

Balloons
Streamers
Hats
Silly String

Both Taxonomies relate to each other. If I were to click on Blue, I want to receive a directory that looks like this:

Blue Balloons
Blue Streamers
Blue Hats
Blue Silly String

If I were to click on Hats, I want to receive a directory that looks like this:

Blue Hats
Orange Hats
Red Hats
Green Hats

If I were to click on the Blue Balloons it would take me to a custom single-{custom-post-type}.php I’ve created for party favors. In that post, I would like to be able to query the terms “Blue” and “Balloon” and use them throughout the content in the post.

How do I do all this?

Thanks in advance.