The one thing we know for certain is that holding large amounts of cash isn't ideal - inflation will eat away at your wealth.
It's understandable that you're hesitant to put all your wealth in common stock. The S&P 500's price/earnings is 18.7 right now - a little high by historical standards. But consider that the S&P 500 has given a CAGR of approximately 10% (not inflation-adjusted) since 1970. If you don't time the market correctly, you could miss out on considerable gains.
So it's probably best to invest at least a portion of your wealth in common stocks, and just accept the risk of short-term losses. You'll likely come out ahead in the long run, compared to an investor who tries to time the market and ends up holding cash positions for too long.
If you really think US stocks are overpriced, you could look at other markets, but you'll find similar P/Es in Europe and Japan. You could try an emerging market fund like VEMAX if you have the risk tolerance.
Let's say you're not convinced, and don't want to invest heavily in stocks right now. In the current market, safe cash alternatives like Treasury bills offer very low yields - not enough to offset inflation tax. So I would invest in a diversified portfolio of long-term bonds, real estate, maybe precious metals, and whatever amount of stock you're comfortable with.