My computer, as I've mentioned, is old. I've rebuilt it a couple times with new components, and upgraded to newer versions of windows over the years. My hard drive has always had a partitioned d:/ drive set as a recovery drive, from when it was running windows 7 (if that tells you how old it is). As far as I can tell, windows 10, which I'm currently running and wanting to get rid of, can't do much of anything with the recovery drive; it insists that I only need OneDrive for a backup (which I refuse to use).
I've been test-driving MATE on a usb boot, don't panic yet. I am going to be getting an external hard drive to back up all my files and media (almost a decade's worth) before I do ANYTHING I'm asking about here.
But.
When I have everything ready, what's the safest way for me to de-partition the old hard drive and free up all that d:/ drive space? Is there anything I need to know before I do it so it doesn't break my system? I do have windows 10 boot media on a USB drive as well, just in case. I'm reading through the GParted partition guide in suggested posts, but that's from 2017 and I expect things have changed a bit since then.
Gparted remains a very good tool, I mount some old drive on my Linux and use gparted to wipe out every partition I can find, format the disk ext4 and verify all is good. There are many other tools, dd, wipefs, ...
You didn't mention whether you were planning to have a dual-boot or Linux-only configuration. Care to share?
- Default installation procedure would wipe out the whole drive for you automagically.
- What flavour of 'safety' is being meant?
- You might want to install
Virtualboxfor Windows or another virtualization software to try and test installation procedure using a virtual machine.
gparted is my go-to tool for all things partition. That d: drive is just another partition - it's not 'd:' to anyone but Windows - that's how they mount drives. But it's just /dev/sdxy to Linux and gparted, and you can reformat it to, e.g., ext4, and use it as a data partition. Or depending on the drive layout, maybe merge it with another partition, if it's contiguous.
If you will be dual booting with Windows, you can format it to ntfs, and use it for shared data between Windows and Linux - that's what I do.
What is your goal here?
I am planning on moving to a linux-only configuration unless it later becomes necessary to put up with Microsoft's intrusions again. I don't do anything with my computer that requires any of microsoft's proprietary programs
In some of my searches for information, I saw things about the partition being "locked" for use by windows, and therefore unable to be accessed or reformatted unless certain configuration changes have been made.
My goal is to get Microsoft off my system and out of my data and my business
I have never heard of or stumbled on situation when low-level partitioning tools could not wipe out some partition and/or repartition a drive while installing OS.
That's a relief, thank you!
I think he is getting confused. Bitlocker locks the Windows partion from Linux.
Linux installation performs a "full takeover" of any target drive, unless you intentionally configure a dual-boot, in which case things get hairy and scary!
Best to keep it to a clean single-boot install and, if need be, get a second disk for the Windows, if you want to keep that in reserve. (or keep the existing disk as-is with Windows, for possible emergencies, and get a "factory-fresh" disk for your "nice and shiny" Linux! 
The Ubuntu (MATE) installer will be able to safely re-partition your hard drive whether you want to go single boot (i.e. take over the whole drive) or dual boot.
If you've got as far as booting onto the live USB then it's almost certain that your machine is ready to tear up anything on the SSD or HDD that you want (i.e. UEFI has passed the keys to your hardware to Ubuntu). Windows, in my experience, won't be able to do anything to 'lock' the hardware to prevent re-partitioning.
You sound like you already know the most important lesson before you start: back everything up just in case! You can use either Disk Image Writer or GParted from the live boot to create the backup on another storage device. There is also a low-level (i.e. bare bones and difficult-to-use) tool called dd which I have used in the past.
Once you have your Windows files backed up, I would recommend installing Ubuntu-Mate on the whole disk.
You can easily create more partitions later.
Take your time and learn Ubuntu-Mate. The learning curve is not bad, and it is safer than Windows.
I have also found you can easily customize it any way you like.
Good luck.
If you're planning on going all-Linux, just use gparted to reformat the "D:" partition to ext4 (the standard Linux filesystem). Or make the whole drive one big ext 4 partition and divide it up later as desired. If this is a UEFI system, make sure you don't mess with the first partition, which is the boot partition.