It's harder than you'd imagine. First off, when you read, you can't sound like your reading. You have to sound normal.
And don't do an announcer voice. Sound natural. You also have to be an excellent reader. It helps a ton. You also have to make sure you do it again and again without sounding burnt out. People always underestimate this part, because it's hard to sound excited about a fucking McGriddle after you flubbed the line four times in a row.
Basically, it's hard. You have to read a shit-ton in 4 seconds sometimes, sound normal despite being given unusual writing that isn't natural, and do it in as less tries as possible.
It's real hard. I'd do an example with my shitty Blue Yeti at home (I go record my actual shit for a studio downtown that hires me) but I'm really warm and in bed right now.
It's very interesting though--much harder than you'd expect.
As to how to get into to it? Well, look for a studio, look for some peoples name--ask around as much as you can. I asked several fellow acting-bros and they eventually pointed me to a man at a radio station. He'd charge me $400 dollars to produce my demo-reel, and when we finished the first one, he gave me a job on the spot. He seemed to think I was good.
Also, if you're going to take it seriously, consider joining an actor's union. That way, instead of getting paid per gig, you can get paid doubled the gig's normal price (so instead of $200 dollars and no more, you then get paid $450 each time it's played and so on). Also consider getting an agent, or joining an agency. If you do vice over independently, you technically own you. Therefore, you cannot supply yourself with benefits, like other businesses can with insurance. Agencies help you with this.
Remember, doing this shit is 80% business, 20% of the actual voice-work. It's all about marketing yourself as a product, and selling yourself.