Yes, I understand Square is a credit card processing service, but I'm trying to figure out how to use it since my business doesn't have a physical location and I really dont need a credit card processing device. 

You have two options if you aren't swiping credit cards. First is Virtual Terminal (https://squareup.com/help/us/en/article/5807-virtual-terminal) which would allow you to enter a card number provided by your customer. The second is Square Invoices (https://squareup.com/invoices) which would require you to send a customer a bill that they could then pay online.  Hopefully one of those will work for you!

I have been looking at the invoice option and I think that will work!  A few questions. . .  How secure is this site?  You only charge 2.9% plus 30¢ per transaction, right?  Lastly, can you put a computer logo on the invoice? 

Security is very important to Square. You can read about the ways they keep your data safe here: https://squareup.com/security

You're correct on the fees. When your customer pays the invoice, the fee will be deducted from the deposit. 

You can customize your invoices. Learn more here: https://squareup.com/help/us/en/article/5424-customize-receipts-and-invoices

I just have one more question, hopefully.  Do you have any suggestions for getting this logo to fit.  I have played around with the dimensions, but I can't get it to fit.  Also, is there a way not to have a background color? 

@mindy1 - This a tad trickier. You'll have to resize the image so it is a square. You'll probably have to use some sort of photo editing tool (online or software). As for the background color, were you talking about the receipt header? If so, we let you chose from 12 different colors from the Receipt editor on the Square Dashboard. Hope this helps!