How do ATM transactions work?

There are a variety of electronic transactions one can execute:

ATMs allow you to bank electronically, get cash, make deposits, pay bills, or transfer funds between accounts. These machines are used with a debit or ATM card and a personal identification number.
Point of Sale Transactions. Some ATM cards and debit cards can be used in stores to charge merchandise. Money is electronically drawn from your account and paid to the store.
Pre-authorized transfers. This is allowing for the automatic deposit of fund or withdrawal of funds to or from your account. For example, one can authorize the direct deposit of wages, social security, or dividends directly to their account. You can also pre-authorize your bank to make automatic transfers for bill paying.
Telephone transfers. You can transfer funds from one of your accounts to the other, or order bill payments over the phone.
Most ATMs provide you with a receipt for the transaction, as do point of sale purchases. These receipts are the records of your electronic transactions and should be kept. Additionally, your periodic bank statement will show all the electronic transfers performed. This monthly statement is your proof of payment to another party and is your record for tax and other purposes. Any inconsistencies can be taken up with your bank.