(My source is primarily Benjamin Roth's depression diary.)
Short answer, optimal in retrospect, but hyper-risky at the time: In hindsight the optimal strategy would be: Sell all you own in 1929 and only own cash. Buy stock for 100% in 1932. Never sell the stock. Live of the dividends. Never borrow money. Excluding dividends this would have a return of 100% by 1938 and maybe 800% by 1950.
Now on to a real answer:
Imagine the crash. Prices plummet as deep as in any crash in living memory. It looks like a recovery sets in. Prices fall even deeper and keep on falling for three years despite a handful of false recoveries until the Dow in 1932 is 15% of what it was 1929. Then comes two decades of recovery but with what looks like grand collapses every few years. 1934, 1937, 1940-1942 and 1946. If you bought at the peak in 1937 you would have to wait until 1950 to get your money back and in between you would see a drop of 50%. http://www.macrotrends.net/1319/dow-jones-100-year-historical-chart
Whatever advice you got in 1929 you would probably panic a dozen times. If you knew a bit of market history from Russia, you would fear a repeat of the very bad day Russian stocks had in 1917 when they fell to 0 and stayed there forever. Politics in the US seemed crazy. Roosevelt forbade the private ownership of gold in 1933 and experimented wildly with new policies. (At one point the federal state went out to slaughter pigs and let the meat spoil as a way to stimulate agriculture.) You could not know if capitalism would last. Russia, Italy and most of Central Europe had turned into dictatorships before Hitler even invaded Poland.
Some weird things that happened during the crisis:
There was deflation. The purchasing power of cash rose by 50%, I may misremember the exact number. Anyway Cash turned out to be the best asset in the US. But keep in mind that a decade before the German Mark lost all its value. You would not trust cash! To protect yourself from the risk of hyperinflation, you would probably want gold
But as stated before Roosevelt banned private ownership of gold.
Real estate sold for a song, but then plummeted to approximately nothing, while the owner had to pay taxes for it.
As said gold ownership became illegal
Banks crashed all over the place. At least where Roth lived banks would not let people withdraw money. If you had a fortune in the banks you could not get it out. People began selling bank-money for cash, at an exchange rate of something like 1 dollar for 50 cent.
Banks became very stingy about loans. If you borrowed money, you could expect the bank to be fierce about getting it back. Many people who borrowed to buy cheap assets in 1930 became ruined when banks demanded the money back.
Talking to somebody from 1929, I think the wollowing message would have made sense to him given what he knew, would make him well of financially, and protect against eventualities like hyper inflation:
Right now prices are higher than ever before. I know, I know technology is awesome and people say the world has entered a new era of increased growth. But people have said so in the past to. Technology and world trade was looking promising in 1880 just as today, but prices did not shoot up like crazy back then. There is nothing objective justifying that prices now are about 3 times higher than in 1916. Profits have not increased nearly as much.
I predict a crash. We have had crashes about once per decade since 1880, but I think this one will be a lot bigger because prices are so high right now. When this crash happens, prices might fall by 70% instead of the usual 30%. 70% would bring prices back to what makes sense from a historic perspective. But of course such a big drop would cause panic, so prices may fall even further.
My recommendation to you is this. Sell your stocks today. Invest your money in gold, foreign currency and regular dollars, you do not want all eggs in one basket. Real Estate is out, because counter to popular belief it falls in crises just like stock.
Buy stock for 40% of your money when prices are I do not know ... 50% of what they are today. (Stocks are after all the best long term investment, even if have average valuations and are not dirt cheap). But be prepared for even deeper prize drops. If prices drop by 25 more percent I think you should invest for an additional 40% of your wealth..
Another thing. We live in volatile times. Lenin, Mussolini, Hitler and the Great War of 1914 to 1918, in case everything goes to hell you better have a back up plan. You might need to emigrate if our country turns nasty too. If you live nearby a foreign country I recommend you have a bank account there ready in case the banks at home go the way of Russia.
Don't hold stocks when the crash comes. Be careful of any banks you deposit with. Sell short- enter into a contract to sell specific stocks in specific quantity at a fixed future (ie post Crash) date when the price has fallen. Be careful to do this only with someone who will be able to pay post Crash.