Patched Sur
OCLP and Monterey
Since I'm not making a Monterey patcher and Patched Sur is being discontinued in 2022, you're going to want to use OCLP to keep up-to-date, whether you want to stay on Big Sur or upgrade to Monterey.
If you want to upgrade to Monterey, follow this tutorial until the end. If you want to stay on Big Sur, follow this tutorial until the Monterey part.
Also side note: Since I'm not doing this on my Mac quite yet, I can't provide many screenshots, so if you want to fix that, just take screenshots as you go and then send them to me.
Other side note: This tutorial is only for people who have Patched Sur.

Switching to OCLP

The first thing you're going to do is download OCLP. You can use the TUI or the GUI (not my GUI, it was designed by dosdude1 based on Mykola's mockups) which are both pretty much the same, but the TUI is apparently more stable. I'll provide instructions for the TUI, but you can easily predict what you need to do with the GUI.
You can download the TUI here and the GUI here. Launch the app, and you should see something like this (as I said, I'm using the TUI, the GUI is obviously different):
Main Screen of OCLP TUI
In the TUI, to select an option, use the number/letter on the far left side of the option and then press enter. For example: If I wanted to select 5. Patcher Settings, I would type in 5 then press enter.

Configuring the Patcher

Speaking of 5. Patcher Settings, that's what we're going to start with. We just need to ensure that two settings are disabled.
So go into 5. Patcher Settings, then go to 2. Security Settings, and you should see a screen that looks like this:
Security Settings of OCLP TUI
In my case, SIP and SBM were both already disabled, but if they weren't, we'd need to fix that.
SIP: Select 1. Set System Integrity Protection then 2. Disable SIP.
SBM: Select 2. Set Secure Boot Model then 2. Disable SecureBootModel.
Note: Vault is not FileVault! It will be off by default, and don't turn it on unless you know what it really is.
After setting those two settings, you can go back to the main screen by selecting Q. Quit then Q. Quit again.

Building and Installing OpenCore

Now that it's configured, we can build and install OpenCore.
To build OpenCore, it's about as simple as pressing 1 and enter. I'm not joking, you select 1. Build OpenCore, and it's done pretty much instantly. After that you just have to click enter to go back to the main screen.
To install OpenCore, you need to select 2. Install OpenCore to USB/internal drive and just choose your internal drive's EFI (you can do a USB, but then your Mac can't boot without the USB).
After that, reboot and hold down option until you see the boot picker. Select the OCLP icon (it should be named EFI Boot) then if that shows another picker, you don't need to do anything (if you happen to click the arrow keys, it won't auto boot, so then you just select your main drive). This popup will show up every time you boot your Mac from now on, so that's why it has auto-boot.
Once your Mac is booted, you can safely delete the Patched Sur app (you want to delete it because it will complain about the NVRAM) and call it day, unless you want to upgrade to Monterey.

Upgrading to Monterey

Now that you've configured, built, and installed OpenCore, you can upgrade to Monterey. The simplest way to do this is that you could just use Software Update, but using an installer usb is much more stable, so I suggest that.

Creating a Monterey Installer

Now, I'm not going to type out how to do that, so here's a video:
Mr. Macintosh's Awesome Video. Like and subscribe, he's cool.

Installing using the Installer

Now that you made your Monterey installer usb, you need to use it. So reboot your Mac again but don't hold option. The OpenCore boot picker will show up automatically, so all you need to do is select Install macOS Monterey when it comes up.
Once it boots, select Install macOS Monterey, and follow through the prompts, accept the software license agreement without reading it, select your internal disk, etc etc. That'll start installing, and then eventually....

Getting Graphics Acceleration

Unlike Patched Sur, WiFi will work right away. But that wouldn't be the first thing you notice, instead, you might notice your Mac is painfully slow and some things aren't translucent when they should be. That's normal, and it can fixed.
Open OCLP again (be patient) and select 3. Post-Install Volume Patch and follow the prompts of that.
Once it's done, reboot your Mac, and everything (should) go back to normal, and you'll be done.