Okay, quick overview.
There is nothing inherently taxable or tax-sheltered about an index fund in itself, it depends on the type of account it's in. Let's define some terms:
Mutual Fund: somewhere you can invest your money where each dollar you invest in the mutual fund gives you a tiny fraction of many different individual stocks.
Managed Mutual Fund: one specific form of mutual fund, a team of researchers and investors that are trying to pick which stocks they should include in the fund to give you the maximum return. You pay them for their services in the form of annual fees that are deducted from the account.
Index Fund: the other specific form of mutual fund. In this case there is no team of researchers, the stocks are chosen automatically via some index. An index will tell the fund how much to invest where, for example if we're talking about an Index Fund that tracks the S&P 500 index and Apple is 1% of the value of that index, then 1% of the money in that Index Fund will be in Apple stock. Because there is no one you have to pay they generally have very low fees.
You can purchase either of these types of Mutual Funds in any account you want. I for example own the same Vanguard index fund in my tax-advantaged accounts (a Health Savings Account, a Traditional IRA, a Roth IRA, and a 401k) and in just a regular non-tax-advantaged investment account.
If you're investing in a regular non-tax-advantaged investment account, then when you sell your shares in the Mutual Fund (this also applies to individual stocks) you will have to pay taxes on the gains - how much more it's worth now than when you bought it. You will be paying what is known as Capital Gains Tax, and how much it is depends on how long you held the investment before you sold it. If you held it "short term", less than a year, you will pay whatever your current tax rate is as if it were regular income. For example, I'm in the 25% tax bracket, so I if I bought an investment today at $1000 and sold it tomorrow at $3000, I would owe 25% of the gains (25% * $2000 = $500) at the end of the year in taxes. If you held it "long term", longer than a year, then you owe taxes at the long-term capital gains rate, which is currently 15% if you're in the 25% bracket or higher or 0% if you're not. In any case, your investment company will send you a form, a 1099-div, that tells you what you have to report on your taxes.
Index Funds are no better or worse than buying Managed Mutual Funds or individual Stocks tax-wise.