Please note: To see some real benefit, don't invest a small amount as what you would get back would be easy enough to get through store robberies and security vans. Instead, perhaps wait until you've finished the story so you have a lot of bank, then do this. The results would be a lot harder to achieve through other means.
Second note: You will however need to complete the first Assassination ("Hotel Assassination") before you can progress the main story past the "Blitz Play" mission. This can cause a small predicament if BAWSAQ isn't working for you, as you'll learn about further down. In this case, you may need to forfeit the money you could make from the first mission, or wait for BAWSAQ to be up and running again.
Third note: Refer to THIS post while following my tips to make even more money!
When you come to do the Assassination missions with Franklin (after "Fame or Shame"), make a Quick Save before you start each mission.
The stock markets are found on the internet. Click Money and Services, and then LCN or BAWSAQ. Click Markets to find a list of companies currently on the market. 2 of the markets we will be using will be on LCN, while the other 2 are on BAWSAQ. (Please note: BAWSAQ requires an internet connection, as the stocks are linked to Rockstar's Social Club. If the SC is down, BAWSAQ will also be down. LCN is an offline stock market and can be used even if the SC isn't working.)
Lester will hint at buying in to these companies during the mission briefing, but once the mission starts you won't be able to switch characters, meaning only one can reap the rewards.
Before the first mission, pour all your money from each character in to BetaPharmaceuticals
(found on the BAWSAQ page, which relies on Social Club actually working). When the mission has finished, head to a safehouse and sleep for about 3 days (sleeping passes time by 6 hours, and I'd recommend saving on a new slot or just pressing B at the save screen), and then sell all of your stocks, because your return will be huge. A really good tip is to check the percentage the stocks are at every game day, and if they're on the rise save on a dedicated new slot. Do that everytime it goes up and you can be as greedy as you like because you can just revert back if things go wrong.
On the second mission, pour all of your money in to Debonaire Cigarettes
, and then do the same as last time. On the third mission, buy in to Fruit
(found on BAWSAQ again). On the fourth mission, don't buy anything. As soon as the mission is over, spend everything on Vapid
as it's just tanked. Keep an eye on it and sell when it goes high again, and then on the final (5th) mission buy in to GoldCoast
You will make huge money, as you will be taking out key targets in their rival companies, making their stocks plummet, while yours will increase exponentially.
You may be able to raise the stocks even further, but after the 3rd day they just seemed to stay at around 81.55% for me. Your milage may vary, of course. I recommend only saving a couple of times up to the 81% mark, and not any further. After this the stocks may go down and you could lose a lot. If they do, reload your save and sell at 81%
This also gets you Trading Pure Alpha
if you haven't already unlocked it.