Do you want to do it pre or post correction?
If you're bearish on the market the obvious thing to do is short an index. I would say this is kind of dumb. The main problem is that it may take months or years for the market to crash, and by then it will have gone up so much that even the crash doesn't bring you profit, and you're paying borrowing fees meanwhile as well. You need to watch the portfolio also, when you short sell you'll get a bunch of cash, which you most likely will want to invest, but once you invest it, the market can spike and pummel your short position, resulting in negative remaining cash (since you already spent it). At that point you get a margin call from your broker. If you check your account regularly, not a big deal, but bad things can happen if you treat it as a fire and forget strategy.
These days they have inverse funds so you don't have to borrow anything. The fund manager borrows for you. I'd say those are much better.
The less cumbersome choice is to simply sell call options on the index or buy puts. These are even cash options, so when you exercise you get/lose money, not shares. You can even arrange them so that your potential loss is capped. (but honestly, same goes for shorts - it's called a stop loss)
You could also wait for the correction and buy the dip. Less worrying about shorts and such, but of course the issue is timing the crash. Usually the crashes are very quick, and there are several "pre-crashes" that look like it bottomed out but then it crashes more. So actually very difficult thing to tell. You have to know either exactly when the correction will be, or exactly what the price floor is (and set a limit buy). Hope your crystal ball works!
Yet another choice is finding asset classes uncorrelated or even anticorrelated with the broader market. For instance some emerging markets (developing countries), some sectors, individual stocks that are not inflated, bonds, gold and so on can have these characteristics where if S&P goes down they go up. Buying those may be a safer approach since at least you are still holding a fundamentally valuable thing even if your thesis flops, meanwhile shorts and puts and the like are purely speculative.