The Bogleheads wiki has all sorts of information to help you get started. The three fund portfolio is what I use--simple, well diversified, and extremely low cost.
Before mid March, I had absolutely no idea how to invest. After reading the Bogleheads wiki and lurking on their forums, I learned basically all I need to know. It will take you time to read through all the important bits. But it's well worth your time, and afterwards you can just set up automatic investments and just let it run without you thinking about it (recently I logged into my Vanguard account and was like how on earth did I accumulate this much? And it wasn't investment returns either - returns only accounts for about 2% of my account value).
Just a small point -- assuming you're already with Fidelity, you don't necessarily need to transfer your money to Vanguard. The Fidelity Spartan index funds directly compete with the Vanguard options and are just fine.
They're competitive at the moment. However, Fidelity could decide at any time in the future to raise the expenses on their funds. If that were to happen, and you held the funds in a taxable account, you would incur capital gains tax to switch to Vanguard's funds.
Vanguard is structured to operate at cost because the clients are also the shareholders of Vanguard. It would be incredibly difficult, unless Fidelity purposely took a loss on Spartan funds and hoped to make it up elsewhere, for Fidelity to beat Vanguard's expenses, because Fidelity needs to make a profit to please shareholders. Vanguard does not.
What's the probability that Fidelity would raise the expense ratio enough for it to be a concern in comparison to Vanguard? Pretty small. But given Vanguard's structure, I would always recommend that when you have the choice, choose Vanguard, because they are designed so they won't try to screw you.