1) Download & Install .NET Framework 4.8 if you're using Windows 7, Windows 8 and above, should do this automatically for you.
2) Extract the files somewhere very safe on your computer. If you lose the files you can lose access to your Steam account.
3) Run Steam Desktop Authenticator.exe and click the button to set up a new account.
4) Login to Steam and follow the instructions to set it up. Note: you still need a mobile phone that can receive SMS.
5) You may be asked to set up encryption, this is to make sure if someone gains access to your computer they can't steal your Steam account from this program. This is optional but highly recommended.
6) Select your account from the list to view the current login code, and click Trade Confirmations to see pending trade confirmations.
7) For your safety, remember to get Steam Guard backup codes! Follow this link and click "Get Backup Codes," then print out that page and save it in a safe place. You can use these codes if you lose access to your authenticator.
REMEMBER: Always make backups of your maFiles directory! If you lose your encryption key or delete maFiles by accident AND you didn't save your revocation code, you are screwed.
IF you lost your maFiles OR lost your encryption key, go here and click "Remove Authenticator" then enter your revocation code that you wrote down when you first added your account to SDA.
If you did not follow the directions and did not write your revocation code down, you're well and truly screwed. The only option is beg to Steam Support and say you lost your mobile authenticator and the revocation code.
Using SDA on multiple computers
You can use Steam Desktop Authenticator on multiple computers at the same time, with the same Steam account(s).
To retain all Steam accounts from one computer, copy the entire folder where you have Steam Desktop Authenticator installed and move it to another computer using something like a flash drive or a network file transfer.
If you already have other accounts setup on a different computer, you can use File -> Import maFile to import single accounts to other computers.