Joe
As far as i know the ASA cannot act as a DNS server nor can it act as a DNS relay. What you can do is -
1) configure DNS servers on the ASA that can be used in certain situations for allowing the ASA to resolve a name to an IP. For example using the Botnet filter on the ASA, SSL certificates etc. require the ASA to be able to qurey external DNS servers.
But this is for use by the ASA itself ie. it is used to resolve names within the ASA config. It is not used to allow clients to ask the ASA to resolve DNS names for them. So it can neither act as a DNS server itself nor can it pass on clients DNS queries to DNS servers.
2) if you use the ASA to hand out IPs via DHCP you can add valid DNS servers within the DHCP config just as you can with Windows DHCP.
Jon