https://personal.vanguard.com/us/openaccount
The above link and 8 screen shots will get you going for opening up an account with them. It's incredibly easy and I was able to do it in 15 minutes for my friend this weekend.
A lot of it is some very basic information that they need to know about you personally. Some questions and road blocks that you may run into are:
Screen 1: choose to open a new account until you want to setup a retirement account or transfer an account from another brokerage.
Screen 3: opt for the general savings account and the individual account type unless you want it to also be in your spouse's name as well. In that case choose "joint".
Screen 6: Choose "no" for both questions a the bottom unless the account owner is a FINRA employee or if somebody close to use is a big wig at a publicly traded company. Meaning they own 10% of the company, they're an executive, or is on the board of directors.
Screen 7: I like the electronic bank transfer the best because it'll allow for you to setup an automatic investment plan. Be sure to save $3,000 first and then start off with that amount for the investment amount.
Screen 8: To make this as simple as possible, just go ahead and select "reinvest". What this means is when your investments pay you dividends (cash payments to the owners) it will automatically buy more of the paying investment.
Now if you're wondering how this will make you a millionaire, it's quite simple. Assuming that you start around the age of 25 and work until 65 and you get manage a very average 8% return. All you have to do it save a measly $321.68 per month. Better yet, just throw an even $100 a week at it and you'll have a nice little nest egg of $1,347,000 when you retire. Super easy. Set it up, automatically draft $100 a week into it and let it do the rest!