I have some really high-availability web page content that needs to be online 24x7. So instead of relying on a single server I was wondering if I could handle one domain name with multiple servers?
Could I just set different nameservers for that domain? Would requests be automatically distributed amongst those servers? Is it that simple?
You absolutely do not want to use Round Robin DNS. The main issue is that it cannot balance load with any kind of intelligence, and it doesn't take into account DNS caching on the client side. DNS is just not meant to do Load Balancing. This technology is deprecated and what you really want to use is a Server Load Balancer (either Appliance or Software, but I really recommend an Appliance if you care about performance).
What happens is this:
Some popular SLB vendors are F5 (my personnal favorite, but that's just me, and they tend to be more expensive - for good reasons, but that's also my opinion), RadWare, Cisco and Juniper.
You really have four options:
The problem with DNS round robbin is if one of your servers go down, every N requests will fail as the try to use that IP.
Only using clustering and/or a load balancer will give you true fault tolerance to hardware failure as they will stop sending requests to the down server.
Yes, it is the basic way to assure load balancing among different servers (web servers)... it is referred as Round Robin DNS.
Pay attention that this is a load balancing technique, it does not assure any failover against single server failure, ie if a server is down and your client is getting its address by the DNS it would have a failure in the connection. Statistically reloading again and again it will have a connection with a working server, but it is not a clean solution.
Something to be careful with when choosing a load-balancing solution is whether your website needs to deal with sessions. If it is the case, make sure you use a load-balancing technique that won't choose servers randomly for a given client, otherwise they might just lose their session on your website by being redirected to a different server every time.