The first hour after your laptop won't boot
What you do in the first hour decides whether your files are recoverable. Most of it is about what NOT to do.
The single most expensive mistake is to keep trying. A drive that is failing mechanically gets worse every time it spins up, and a drive that is failing logically gets worse every time something writes to it.
Stop using the machine
Power it down. Not sleep — off. Every additional boot is another chance for the operating system to “helpfully” repair a filesystem, and a repair that succeeds can overwrite the very blocks your files live in.
Do not run recovery software on the failing drive
Recovery tools that install onto, or write to, the drive you are recovering are working against you. The correct order is: image first, then work on the image.
Write down what happened
When it last worked, what changed, what noises it makes. A clicking drive and a drive that mounts-then-vanishes are different problems with different odds.
What recovery actually looks like
A read-only image of the media, taken once, then every attempt made against copies of that image. The original is touched as little as possible, and there is a record of what was done to it — which matters if the files ever have to stand up to a dispute.