Hard Drive Format
I have a hard drive I took from a windows pc. I have a docking station for it. I want rouse it for backing up my MacBook Air. How do I format it to use it on my MacBook?
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I would not advise you to use a used drive for a backup drive. You want a known good healthy drive for use as a backup drive. Drives used in computers are rarely healthy. When you need to restore a file or your system from the backup you want your backup drive to be as healthy and reliable as possible or the backup drive is worthless. Don't be cheap when it comes to your data. You spent money for your Mac, so don't be afraid to purchase a new drive for your backups.
How you format the drive for a TM backup drive depends on the OS you are using. Traditionally a TM backup drive was supposed to be erased as GUID partition and MacOS Extended (Journaled). With macOS Monterey (and possibly Big Sur) Apple prefers to have a TM drive erased as GUID partition and APFS (top option). Since you want to use a drive formerly used in a Windows' PC you definitely want to make it an Apple friendly drive before doing anything else so make sure to select the whole physical drive to erase which may require you to click "View" within Disk Utility and select "Show All Devices" so that the physical drive appears on the left pane of Disk Utility.
I don't use TM so I'm not certain about all the details. I've heard that macOS will prompt you to erase the drive you select for your TM backup drive and most likely should suggest a default file system. Here is one Apple article about how to use Time Machine:
Back up your Mac with Time Machine - Apple Support