Can you find out what host someone is using by there domain name?

You might get some clue by doing whois lookup and seeing where the nameservers are pointing.

Get the nameservers from a WHOIS then run a traceroute on the nameservers or IP. You may be able to spot the host on one of the last hops. Also plug the nameservers or IP into webhosting.info.

Do a Whois on the domains, as previously suggested - but rathre than do a rtraceroute on the name servers I would do a Whois on the name server domains (e.g., if the name servers are ns1 and ns2.livedns.co.uk I'd do a Whois on livedns.co.uk which will tell me it's Fasthosts)

The only time this doesn't work is when the domain uses glue records (i.e., domainx.com hosted at ns1. and ns2.domainx.com). In that case I would do a Whois on the IP addresses using one of the services that supports this (such as Geektools)

try www.onlinewhois.info (http://www.onlinewhois.info)

there you can see the whois, the IP details, the DNS and so on...