You decide on which fund you want, open an account with the appropriate mutual fund company (e.g. Vanguard) or a brokerage, transfer to them the money from your checking account, and put that money into the fund.
Lumifer’s answered this already in a sibling comment, but note that this general class of question is answered in the Procedural Knowledge Gaps thread (or its repeat). (I wrote a longer answer to this particular question there.)
I want to invest $10,000 in a stock index fund. (The money is currently in a checking account.) How do I actually go about doing this?
You decide on which fund you want, open an account with the appropriate mutual fund company (e.g. Vanguard) or a brokerage, transfer to them the money from your checking account, and put that money into the fund.
Lumifer’s answered this already in a sibling comment, but note that this general class of question is answered in the Procedural Knowledge Gaps thread (or its repeat). (I wrote a longer answer to this particular question there.)
https://personal.vanguard.com/us/funds/snapshot?FundId=0040&FundIntExt=INT
or
https://www.fidelity.com/mutual-funds/index-funds/overview