I like having paper statements. I pay most bills online, but I use the statements as a guide. When bills come in they go in a stack on a certain place on my desk. I know where they are so I always know when I have bills due. I pretty much have it in my head what is due and when. My car ins comes out automatically on the 4th of the month, so I automatically enter that in my check register, along with a service fee I pay to the bank for online banking. I take that out automatically.
Now that I get paid every 2 weeks I take the car ins out of the first check and the bank fee out of the second one since its towards the end of the month.
When I get paid I look at the stack of bills and pay what I can. I write on the statement "paid" and deduct it from my check register, and write the confirmation if its an online or phone payment.
Once a bill is paid it goes in a plastic drawer on my little organizer thing. I'll keep the statements for 2 months and then shred them. (I used to save EVERY statement. I'm now shredding years worth of statements.)
The most important thing for me is my check register. I keep diligent account of it. I write everything down that I use my debit card or checks for. When I make a debit purchase the receipt goes in a certain place in my wallet. Every few days I balance the checkbook and check it by the bank online. I haven't overdrawn my account in years now because of this, even when I wasn't working and Grandma was giving me just enough for bills and food.
If you keep your check register balanced and pay only what you can with the money in the bank, thats the best way to go.
(I come from a family of accountants, I love this stuff.

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Oh and I almost always use a calculator. Sometimes I'll be bored at lunch and deduct receipts and if I do it by hand there's more chance of error so I use my cell phone calculator.
Keep a registry!!! Thats my biggest tip.