Yes compound interest has incredible power, but in the equity market there is no direct "compounding" like there is in, say, savings accounts, where you earn interest on top of the interest that is saved.
In the equity market, compounding is "built in". The math is the same, but instead of you getting paid interest directly, you are relying on the companies you invest in to use the profits that they make to grow their businesses year after year, earning even more profits as time goes on.
For a more concrete example, say the entire equity market consisted of one company with a market cap of $1,000,000. Every year the company earns 10% of its value in net profits, so after one year the company is worth $1,100,000, after two tears it's worth 1,210,000 etc., just like if you had a savings account with $1,000,000 that earned 10% interest.
(Obviously, though, the equity market doesn't guarantee any gain year after year, but it illustrates how compounding works in equities).
So, to take advantage of "compounding" in the equity market look at other questions on this site about getting started in investing. There are too many variables to give a good answer at a personal level (how much cash do you want to keep on hand for emergencies? Do you have a 401(k) or other tax-advantaged option? What's your risk tolerance? What's your investment horizon? Do you have any debts that need to be paid first?) but the stock market (overall, not necessarily individual stocks) is an excellent way to build up savings over time.