Making a bank deposit has relatively mundane requirements for the most part. In general, these requirements can be summed up as: (1) provide a deposit slip with the necessary information and (2) ensure that all checks being deposited are endorsed properly. So long as those checks and any deposited cash are together in an envelope, for example, one should be able to make a bank deposit with little to no difficulty.
This first requirement, concerning deposit slips, is relatively easy to manage. While not required under banking laws, most banks have large supplies of generic deposit slips in the bank proper. Obtaining one of these slips and making a bank deposit with it are fairly simple tasks, especially when done with the aid of a teller. Having a teller assist in filling out a deposit slip will further protect a deposit, as it will ensure that the deposit slip is filled out properly for an amount verified by another person.
Deposit slips should usually contain all pertinent information for a given bank deposit, including the name of the depositor, the amount of money being deposited, both as a total, and as separated out between cash and checks, the account number of the checking account into which the bank deposit is going, and the date. Bank deposit slips may also require a signature from the depositing party, though this is not always necessary.
If you were looking for cash back from your bank deposit, which is allowed under banking laws, then you could mention it on the deposit slip. Doing so will likely require you to present some form of ID to the teller when submitting such a deposit, but otherwise should cause no difficulty.
In terms of ensuring that checks in a bank deposit are endorsed correctly under banking laws, the best way to endorse checks intended for a bank deposit is with a restrictive endorsement bearing the terms "for deposit only". Adding "for deposit only" and an account number to the check ensures that the check can only be deposited into that one specific account when it is endorsed, and therefore, would protect the bank deposit under banking laws, specifically the Uniform Commercial Code.
After the bank deposit is submitted, the bank then has certain requirements which it must follow in terms of making the deposit available to the depositor. The Expedited Funds Availability Act (EFAA) of 1987 defines the amounts of time over which a bank can hold a check without making its funds available to the depositor. Even a bank deposit made at a non-proprietary automatic teller machine must be made available to the depositor after a certain amount of time, normally only five days.
The primary determinants of how long a given check can be held are whether or not the check is from a local bank, meaning one with a local transit number, and the amount of the check. Once funds are made available, then the depositor is allowed to draw on those funds without difficulty, whether for cash withdrawals or drawn checks. Banks can still manipulate their own requirements somewhat, however, in attempts to push accounts into becoming overdrawn, but they are limited thanks to banking laws like the EFAA.