Consider setting up a separate checking account for your writing business; keeping writing-related income and expenses separate will make it easier for you to keep track of them. Avoid paying cash for writing expenses; if you must, establish a petty cash fund, putting money in the fund each month and keeping receipts for cash outlays.
You’ll need to keep a filing system for all your receipts so you can verify expenses at the end of the month. A budget sheet for each month can help you keep track of any problems arising in your writing business—what expenses are exceeding expectations, which markets aren’t buying as much as you had planned, etc. A file for submissions helps you keep tabs on your marketing track record: what you submitted where, how long ago, what you were paid, etc.
Make sure you have documentation for each business transaction, such as a canceled check or a cash receipt. You should write the business purpose on the receipt or check.
These simple procedures will get you started. As your writing business gets more successful, you’ll probably want to consider a more detailed system. Many computer software companies make programs that help keep track of finances; Quicken is most well-known in this area.