How to programmatically fill out a form on another site, click a button, pull content for yourself?

Question

PHP

I am a student, I am doing a term paper - the site "Search for Books in Moscow Libraries". The idea is this: on the main page there is a “Book Title” field, the user writes the title, presses the button, the site searches for the book in the electronic catalogs of libraries and on the new page displays the book and which libraries it is in.
My first task is to connect a library for youth (RSLL). How can I automatically fill in the corresponding field “Title” in the form of the RSSL after clicking the button from the “Book title” field on my site , press the “Search” button and display the search result on my site?
My knowledge of PHP ends with the following: get-, post-parameters, cookies, simple work with the database. I don't know if it's possible to automatically fill out a form on other sites, pull someone else's content. But I want to learn this, so I will be glad if you tell me what to do, read, use.