Open an account with scottrade.com and deposit the money there. Then buy VTSMX, which is the Vanguard Total Stock Market fund. Basically, it distributes its money equally throughout the stock market, so you don't have to worry about picking stocks. If you're going to retire in the next 30 years, you might also put some money in a bond fund such as VBMFX. A rule of thumb is that the % of your money that should go into bonds should be equal to your age.

You should also start an IRA, which is a special tax-sheltered account where your money can grow without paying taxes on it. The disadvantage is that you can only put in $4000 per year (will be $5000 soon), and that you can't withdraw it until you're 65 without a penalty. Search around for more info.

This all assumes you won't need the money for the next 5 years at least. There are other options if you anticipate needing it for a down payment on a house or your kids' college tuition.

Do you really need to keep the other $20,000 in your checking account? You could probably open a money market account with ING Direct and get 3% interest on $15,000 of that. A money market fund doesn't pay much interest, but you'll never lose money at it, and you can withdraw your money any time. ING makes it really easy to transfer money between your account with them and your checking account.