You generally use them at the end of a line but it is more accurate to say you use them at the end of a statement but we usually put each statement on a single line so it is easy to make that mistake example:

<?php
$x = 5; // Semicolon ends the statement
$y = 10; // Another statement ends here

if ($x < $y) { // No semicolon needed here
    echo "x is less than y"; // Semicolon ends this statement
}

$x = $x + $y; // Statement ends here
echo $x; // Outputs 15
?>

Wikipedia has some examples; they are always super helpful in cases like this.

I use them after worrying about being pretentious, but then (sometimes) deciding “fuck it. It’s right.” and then doing it anyway.

You can use a semicolon wherever you’d logically break in a sentence, without pausing overtly, but intend to follow the thought; semi-colons slip naturally into your thought process when you practice it by speaking.

Same. I was taught in school but never learned how to use them until I read this (The Oatmeal).

I have one easy rule, and two examples. Use them when using a comma would be confusing.

Examples: often in lists, where each item might contain a comma and so trying to separate list items with commas would just be confusing; and more broadly anywhere where you have a sentance containing clauses and need a different separator.

I just used the first example above: to separate the two list items, and the other one I’m using here, where I’m already using commas; using a semicolon allows braking this up without starting a new sentance.

That second example was somewhat contrived, but does the job; it could have been two sentences.

Actually, there’s another place I use them, but it’s not a “rule” and if more style: I use them selectively in place of periods to prevent a series of short, choppy sentences.

You would use a semi-colon in places where a comma and a colon would be equally suitable, pretty much.