It contains basic methodology for post exploitation.
You should approach to first machine in AD as regular standalone windows machine. Lateral movement or privilege escalation as well. Movement is not so hard. You must do post exploitation very well.
You can do post exploitation steps as follows:
Check groups where the user is in. Check the user in some privileged group.
Check another users in the domain.
Search files in the system for finding passwords, important notes and information, mail etc.
Check services on the system.
Some services contains cleartext passwords, hashes in some files.
Extract hashes, secrets, kerberos tickets with mimikatz etc. (requires system shell)
Try pass the hash methods like using psexec or crackmapexec from impacket, evil-winrm, xfreerdp etc. (If the target user has not Administrator rights, you cannot get shell with impacket).