There are a couple of tools you can use to help you see if things are configured correctly. There are web front ends available for them but I am more familiar with command line variants so that is how I will describe them below.
Check with whois where the domain is currently hosted
To get the information for this site you would use the command "whois serverfault.com"
This gives the response (trimmed for brevity):
Domain Name: SERVERFAULT.COM
Registrar: GODADDY.COM, INC.
Whois Server: whois.godaddy.com
Referral URL: http://registrar.godaddy.com
Name Server: NS21.DOMAINCONTROL.COM
Name Server: NS22.DOMAINCONTROL.COM
This information shows the information that the builders of the .com zone file (internic) hold. It also shows that further information is available from the Godaddy whois server.
If this output does not show your new Registrar and name servers the transfer is not yet complete and you should contact your old registrar.
If this shows your new registrar but not the correct dns information the transfer has been done wrong and you should contact your new registrar.
If the details are correct but the site isn't working then either the .com top level zone has not yet been updated and you need to wait, or the new name servers are not set up correctly. To find out which use the command "dig"
First check the GTLD servers (authoritive for .com):
"dig ns @a.gtld-servers.net serverfault.com"
The results give:
;; QUESTION SECTION:
;serverfault.com. IN NS
;; ANSWER SECTION:
serverfault.com. 172800 IN NS ns21.domaincontrol.com.
serverfault.com. 172800 IN NS ns22.domaincontrol.com.
;; ADDITIONAL SECTION:
ns21.domaincontrol.com. 172800 IN A 216.69.185.11
ns22.domaincontrol.com. 172800 IN A 208.109.255.11
If this information is correct you can continue to do the same query against your new providers DNS:
"dig ns @ns21.domaincontrol.com serverfault.com"
;; QUESTION SECTION:
;serverfault.com. IN NS
;; ANSWER SECTION:
serverfault.com. 3600 IN NS ns21.domaincontrol.com.
serverfault.com. 3600 IN NS ns22.domaincontrol.com.
;; Query time: 76 msec
;; SERVER: 216.69.185.11#53(216.69.185.11)
;; WHEN: Mon Jun 1 16:47:51 2009
;; MSG SIZE rcvd: 85
If this is showing the correct information then you likely have a caching problem and will need to wait for old entries held on caching name servers to expire.