How can I keep a score counter of how many points the player has collected on the screen?

Questions & Answers
1

I want “Score:” and then the score to increase with each collision/pickup of the object.

More specifically, I want "Score: " to become “Score: 1” after picking up a crystal shard, “Score: 2” after picking another, and etc every time the character picks up a crystal shard.

I’m quite new to scripting, and Javascript would be preferred, however C# is fine too.

2

You could create a canvas with a Text element inside.
In your script, make sure you are:

using UnityEditor.UI;

And then you can define

public Text yourTextObject;

Drag and drop your text element into the section in the inspector.

In your code, if you have an int variable called score

private void Update()
{
    yourTextObject.text = "Score: " + score;
}

To update the on screen score every frame.
Hope this helped!