The ASA cannot perform DNS services. However, the ASA can serve as DHCP server, though.
You will need a DNS server configured somewhere else on the AD network. It is usually advisable to configure a primary and secondary. Most MS AD network clients (Win 7 for example) can accept up to 3 DNS entries during DHCP assignment.
After you set up DNS server, it's a simple command on the ASA to point to DNS under DHCP configuration - "dns-server 10.10.10.1 10.10.10.2 10.10.128.31", for example. This lists, in order of priority, 3 DNS servers that will be sent to clients upon DHCP assignment.
Hope this helps,
David