This can be done by load balancing (specify 2 A records in your DNS zone, make sure 2 IPs are on different servers) however it doesnt work with sites based on database unless you have your database hosted at one 100% uptime server.
Cheap Web Hosting - Multiple Domain Hosting - Reseller Hosting - Virtual Private Server
Your zone records should be identical across nameservers; if you have a secondary DNS it only ensures high availability of DNS. It is not advisable to have one nameserver point to one IP and another to another IP, because nameservers dont work in a linear fashion [that is ns1 is queried and if it is down ns2 is queried]
If I remember right, all nameservers are queried simultaneously and the first one to return a result is used
Offering Managed Servers - for an exclusive clientèle who value uptime, caring support and superior technology.
Motley is onto something here. If you use the 4 name server method, it works by querying the quickest responding name server meaning if you want your backup site just for back ups this is not a really good idea.
While adding the extra A record to the DNS for 2 name servers isn't exactly "load balancing" as NetworkData says, its still a very viable backup solution.
No solution can guarantee 100% uptime ( as far as I know ) but the second method would probably be your best bet. We have clients using this method and they are generally quite happy with the results.