The overnight money market refers to the market where banks and other institutions lend and borrow money on a very short term basis, usually overnight. As an individual investor, there are limited ways to directly invest in this market. However, some money market mutual funds and ETFs provide exposure to overnight money market rates. By investing in these funds, individual investors can get returns similar to the overnight money market rate.

Invest in money market mutual funds
Many money market mutual funds invest significantly in overnight repurchase agreements and commercial paper which generate returns based on the overnight money market rate. By purchasing shares of money market funds from leading fund managers like Vanguard, Fidelity or Charles Schwab, individual investors can gain exposure to the overnight market.
Consider ETFs tracking money market indexes
There are ETFs like the iShares Short Treasury Bond ETF (SHV) which track indexes composed of short-term US Treasury securities maturing in less than 1 year. Since the yields on these securities are strongly correlated with prevailing overnight money market rates, such ETFs can be used to invest in the overnight market.
Use money market deposit accounts
Banks like Citi, Wells Fargo and HSBC offer money market deposit accounts which pay out interest based on prevailing money market rates. These accounts function similar to savings accounts while providing yields comparable to the overnight money market.
Indirect exposure through ultra short bond funds
Actively managed ultra short bond funds invest in bonds with very short maturities, sometimes less than 90 days. By holding securities correlated to the overnight money market, they provide indirect exposure to overnight lending rates.
As an individual investor, the easiest way to gain exposure to the overnight money market is to invest in money market mutual funds or ETFs that hold short-term securities paying interest based on prevailing overnight rates.