I wont't say that the stock market doesn't depend on the economy at all, because that's also obviously incorrect. A total economic collapse (think dollars stop being worth money) would obviously affect the stock market just to list a limit case. But on the margins, no, the economy doesn't move the stock market in any appreciable fashion in the time frame a trader operates. In the extremely long term though the health of US capital markets is a function of the size and broad diversification of the US economy.

Operationally speaking, the market moves based on the actions of market participants and thus the primary intellectual challenge is predicting those actions. Since currently the Federal Reserve working in concert with the US Treasury is an active market participant with unlimited capitalization that is telegraphing its moves, that is what's moving the market. Literally nobody trades on the reality that thousands of small businesses are in danger of going bust. Personally I think it's awful, but I don't have the capital to fix it.