I am waiting for one of my old employers to send me my W2 form, I am wondering if I will have to pay a fine if they do not get it to me in time to finish my taxes today?

Only if you have a tax due.  There should be no penalty if you get a refund.  

To find out if you owe a payment, *estimate* your income, you should have a good basis for that in what you were paid last pay period and info about past changes - calculate the total estimated income for 2022 - plug it into the software and see what you owe!

You could even round up any payment due, if you overpay that credit is still yours, right?

With IRS it is more important to send in a payment and show good faith than being exact !!!

Just so you are clear on this....online tax preparation and e-filing close down at midnight tonight, so if you have not filed your 2022 return by then, you are going to need to purchase and download the desktop software to a full PC or Mac, and mail your return.   You will not be able to e-file.