Index funds typically pass the dividends on to the investor. Each quarter (usually) you'll get the dividends paid by the components of the index the fund holds. That may not exactly match what you'd get if you held all the components of the index individually, because index funds sometimes don't hold exactly every component in the exact right proportions, to reduce trading costs or taxes (at least in the US). Note that when you bought the index fund you may have set it up to reinvest dividends, so you won't see the actual cash, but you're still getting the dividend, it's just being used to immediately buy more shares.
As you say, the exact details depend on the fund, but the above is how the "typical" index fund works.
Leveraged index funds are more complex. You may not get any or only a small dividend from them, because they use derivative instruments like options and futures to get the leverage, which don't pay dividends. However, I have seen funds that leverage the dividend as well, although I don't know how they manage that.