What are mutual index funds and how do I invest in them?

Index mutual funds are made up of the stocks in a given index, ie. the S&P 500 Index funds will own the stocks in the S&P 500. The only time trades are made by the fund occur when a stock is dropped from or added to the index, thus keeping trading costs low. You can buy an index fund from any brokerage firm or directly, in some cases, from the fund sponsor.
If you opt to buy an index fund in a taxable account, I suggest you look instead at Exchange Traded Funds (ETF's). You will find they trade against the same indexes, but you will have more control over your tax situation by investing in an ETF. Also, learn the difference between a capitalization weighted index fund as opposed to an equal weighted index fund. Over the past several years, the equal weighted S&P 500 index funds have appreciated more in value than the cap weighted S&P 500 funds, even though they own the same stocks. You will need a brokerage firm to trade ETF's.

These are mutual funds that will track benchmarks. For example, there are index mutual funds that track the S&P 500 index. They are made up of the same stocks held within the S&P 500. Index mutual funds are almost always lower cost then other type of mutual funds. Vanguard pioneered the index mutual fund market. Fidelity also has index funds call Spartan funds.