Avoiding use of a global database handler variable in PHP, to someone who is new to OOP?

Question

EDIT: This question is not a duplicate. Here's why. None of those answers were in the least bit helpful because I completely new to OOP - I need an answer tailored to my level of understanding. Just because the question appears to be similar, the asker is not - not to mention I specifically requested an 'understandable' answer in the first place.

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I'm still reasonably new to PHP overall, and even newer to Object Oriented PHP, having only just started educating myself on it within the past week, and I am still unable to grasp some concepts such as inheritance and what class abstraction is - some of it I've been able to pick up reasonably quickly as I've been working with PDO to handle my database connections and queries for a while now, but otherwise I'm still a newbie at OOPHP, so bear with me if my question seems a bit 'basic'.

I've got an initialization file (init.php) required at the top of each of my webpages, which, among other things, connects to a MySQL database using PDO as such:

try {
    $dbh = new PDO(conn. data here);
} catch(PDOException $e) {
    echo $e->getMessage();
}

So, as I understand it, on execution of this code, $dbh is now instantiated as a PDO object. At the bottom of my init.php file is a much of requires linking to function files, such as user.func.php, images.func.php, etc.

The problem is whenever I need to query the database from inside one of my functions, I need to declare $dbh as a global before I'm able to manipulate it, like so:

function myFunction {
    global $dbh; // Here's the problem!

    try {
        $stmt = $dbh->prepare(Some SQL here);
        $stmt->execute();
    } catch {
        // etc. 
    }
}

Now, the problem is not my understanding of why I have to declare as a global - I understand that much, but how I can avoid it. I've read some StackOverflow answers on why to avoid globals, I'm just not sure how.

How would I go about removing global $dbh from my code? Would I create a database handler class and pass my connection settings to the constructor method each time I instantiate it and use that instead? (Seems a bit redundant).

Not really sure how to replace my use of global variables, so help I can understand is definitely appreciated!