How do I transfer my scores between computers?

As with any other type of file. You can save on a usb stick (and keep as a backup copy) to copy to the default folder (See:Preferences) of the new pc.

Same way like you transfer all other files, like pictures, documents, music files, etc.
So not related to MuseScore at all.

Note that if you are asking that question, that seems to show that you have never considered saving your files somewhere else than your computer.
I don't know what time youve given to your MuseScore work but never saving your files somewhere else than your computer is taking a big risk of losing everything in case of hard disk failure.
I would highly recommend to take, at minimum a regular backup on USB stick or disk.
Then more conscious people would save the backup in another house in case of fire, that's also a possibility.
Especially e.g. if all your family pictures are on that backup as well.

Since you are using Windows, I highly recommend you simply take advantage of OneDrive, bulit into Windows and enabled by default on most systems as far as I know. If you were using OneDrive for your Documents folder on your old system, you woudn't even have to ask this question - as soon as you set up your new system and logged in, your old files would automatically be downloaded and you'd be practically right back where you were. if you disabled OneDrive on the old computer, it's not too late if you still have it, just enable for Documents on both computers, then sit back and wait while the cloud takes care of the rest.

I think Ian may be unsure of something that experienced users are not thinking of.

A score is just a file with a name like "foobar.mscz" and nothing else. There is no necessary associated data stored elsewhere, or embedded in some other Musescore files. So just copy that file and if the Musescore program is installed on the new computer, everything will work.

There are other kinds of applications (nothing to do with ms) where you would need all sorts of other stuff migrated over, so it's a reasonable question.