To enable ASDM on Cisco ASA, the HTTPS server needs to be enabled, and allow HTTPS connections to the ASA.

To configure ASDM (HTTP) access to Cisco ASA on particular interfaces, where core and management are the nameifs use following commands:

ASA(config)#aaa authentication http console LOCAL
ASA(config)#http server enable
ASA(config)#http core

Remember to create username, password to be able to authenticate to asdm:

ASA(config)#username admin password secretpassword