Nothing makes an IRS agent go weak in the knees faster than good records. Copies of things like receipts, utility bills, invoices, billing records, and so on will go miles in helping you prove any deduction, including a home office deduction. Of course, you don't want to spend all of your time filing every little piece of mail you get, so what are you supposed to do?
The answer is electronic records. There are complicated systems out there, but the easiest and cheapest is to just get yourself a scanner. Any scanner will do, but one with a sheet feeder that makes double sided copies automatically is the way to go. (If you can't afford it, a more basic model will do for now, but you'll have to be more disciplined, because it won't be as easy.)
Every time you get a bill that has anything to do with your home, run it through your scanner and scan the whole bill. You don't need the ads that were inserted in the envelope, but scan the bill, the fine print on the back, and even the coupon you are supposed to use to pay. Make sure you fill out the coupon before you scan it. You can scan the check if you want to, but it is probably easier to just make a note of the check number on the payment coupon. Then, you can download all the copies you need at the end of the quarter.
Save the image of the bill to a folder on your computer called Home Office Deduction inside the folder where you keep your business records. Now, when it comes time to claim your home office deduction you can use exact numbers and not guesses.