Inserting an HTML fragment in an online store page

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I am brand new to Shopify and I need to find out if I can do what I have in mind.

I want to create a custom page for a store that contains a form that is used to search my own site and display the search results in the online store page.
Ultimately, the search results will be linked to products to add them to the cart but I'm nowhere that that point yet.

After reading everything I can find on Embedded Apps, App Bridge and App Extensions, I understand many of the concepts but I am still unclear how to put the pieces together. 
In the article Display dynamic store data with app proxies ( I understand the proxy concept but I don't know where the prefix subpath comes from.
If I were to try to duplicate the example in the article, where would "" be defined?
Is this just link in the page?

I'm also unclear on how App Bridge is invoked.

I have searched for sample code to get me started but have come up empty.

I apologize for my thick-headedness and I would be grateful for any guidance.