I would like to know how to enter an agreement with a bank to accrue interest in exchange for 'borrowing' my funds overnight. Anyone familiar with the process?
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This will happen automatically when you open an interest-bearing account with a bank.
You didn't think that banks just kept all that cash in a vault somewhere, did you? That's not the way modern banking works.
Today (and for a long, long time) banks will keep only a small fraction of their deposits on hand (called the "reserve") to fund daily withdrawals and other operations. The rest they routinely lend out to other customers, which is how they pay for their operations (someone has to pay all those tellers, branch managers, loan officers) and pay interest on your deposits, as well as a profit for their owners (it's not a charity service). The fees charged for loan origination, as well as the difference between the loan interest rate and the deposit rate, make up the profit.
Banks rarely hold their own loans. Instead, they will sell the loans in portfolios to investors, sometimes retaining servicing rights (they continue to collect the payments and pass them on) and sometimes not (the payments are now due to someone else). This allows them to make more loans.
Banks may sometimes not have enough capital on hand. In this case, they can make inter-bank loans to meet their short-term needs. In some cases, they'll take those loans from a government central bank. In the US, this is "The Fed", or the Federal Reserve Bank.
In the US, back around the late 1920's, and again in the 1980's some banks experienced a "run", or a situation where people lost confidence in the bank and wanted to withdraw their money. This caused the bank to have insufficient funds to support the withdrawals, so not everyone got their money. People panicked, and others wanted to take their money out, which caused the situation to snowball. This is how many banks failed. (In the '80s, it was savings-and-loans that failed - still a kind of "bank".) Today, we have the FDIC (Federal Deposit Insurance Corporation) to protect depositors. In the crashes in the early 2000's, many banks closed up one night and opened the next in a conservatorship, and then were literally doing business as a new bank without depositors (necessarily) even knowing. This protected the consumers. The bank (as a company) and its owners were not protected.
The easiest way would be to set up a common savings account. Most of them pay some meager interest rate, and over one night it would be especially meager.
A Certificate of Deposit is another way, but you'd have to lock the funds in for an extended period of time.