People 'don't' normally do this. That level of fault tolerance can be done a variety of ways, all expensive, all complex. It's a nice ideal, but don't waste your time. You're not amazon (neither am I :) ).
Here's the route to take. First, assume you get a good hosting company. That means from the internet right up to your webserver things should work fine all the time. Most decent hosting companies are at this level now; my hosting company probably hasn't had unscheduled outages for years. So don't worry about that, just get a good hosting company.
Secondly, web hardware tends to be pretty robust. If you're colocating, get a good server. If you're a bit retentive, buy two servers and keep one offsite for spare parts. I do this, but most people don't. My server's been running for years, no problems. So now I own two out of date servers instead of one :). But I knew if I needed a power supply or memory stick, I had one right there and could get it installed in the time it takes to get to the data center. Risk on this is pretty low to negligible for most people.
So, the internet to your computer is pretty robust. Your webserver hardware is robust. Where you're really going to get screwed on downtime is the information and files ON the webserver. That's prone to hacking, failure, and more likely D'Oh! as you do something stupid like delete some files. While the other things are unlikely to happen, if there's anything that's guaranteed about websites, it's that you're going to screw your own data someday. So it's that level that you need redundancies, backups, archives, all that.
There's a variety of ways to approach this, but basically you want something that gives you a complete, current and easy to access duplicate of the content on your webserver. Complete, current and easy are all variables that you'll need to decide on how much work and effort you want to put into it.
Some folks just keep backup copies somewhere else online. Me, I backup nightly offsite, then keep easy to access copies of each nightly build for a couple of months, then I have a once a week archive copy elsewhere for copies prior to that. For me that works well. I change most files rarely so if I screw up, get hacked, whatever, I pull the files from last night or the night before. Anything from today has potential of being lost - but I'm OK with that for my business.
The alternative is for you to spend $20,000 to cover the risk of you maybe being offline for an hour in the middle of the night, and the likelihood of that happening is one in a million over the next 5 years.