How to transfer data on a laptop to SSD?

I have a Lenovo Ideapad U530 Touch, and it recently broke. (The laptop won't close, but the screen works) I'm hoping to get a new computer soon, and I'm going to get a desktop so I can upgrade my hardware, unlike a laptop.

So here's the big question: is there a way I can take all the files from my current laptop-including OS- and move it onto an SSD so that when I get a new computer I can use the SSD and keep all my files and the OS?

Personal files, yes. The "OS" (assuming some Windows?), no transfer is allowed. That OS came with the Lenovo, sold with it, and goes away with it. It is an "OEM" version and licensed to only that machine.
You will have to use the "new computer" with an OS that either comes with it or that you buy. Windows 10 prices vary from $120 through $230 depending on version.

Download macrium reflect and you can clone the drive to another drive, keeping the O/S and the data with everything saved, you can also buy an adapter and use the same drive in a desktop