Generally when you get that kind of money, well honestly most people just lose it because they have zero financial skill. There have been several books written about how lottery winners just crash and burn, and end up much worse off than when they started. Read the book "Money for Nothing" by Edward Ugel for more on that.
However, for those who do have financial skill, they "diversify, diversify, diversify" - essentially, they do what a university does with its endowment. The stock market is the easiest part - simply buy index funds that own the whole market or a specific part of it, aiming to keep the internal fees within the funds very low. You can read John Bogle's book "Common Sense on Mutual Funds" for why that's a good idea.
Real estate is another popular investment.
Many people want to charge you for handling your money, however their fees and expenses are a guaranteed loss. They feel that because they are financially skilled and you are not, they are entitled to 1-5% a year of your money. Financial skill allows you to minimize those and shield yourself from swindlers. It's a must-have if you win the lottery.