You can access the ASA appliance using telnet , ssh and https through ASDM to Cisco ASA Firewall.

To activate ssh access to ASA you need to have at least:

• username and password which will be used in authentication process,
• AAA lists definition that specifies the source of authentication – they can be retrieved fromRadius server, TACACS+ server or LOCAL ASA database
• Crypto key pair defined for encrypted traffic to work

So to enable SSH:

• Define local username and password:

ASA#configure terminal
ASA(config)#username XXXX privilege 15 password YYYY

• Define AAA lists for ssh:

ASA(config)#aaa authentication ssh console LOCAL

• Generate crypto key pair to use with SSH server:

ASA(config)#domain-name aviumssolutions.com ===> (Example)
ASA(config)#crypto key generate rsa general-keys modulus 1024

In addition you can set the allowed sources, and define on which interface ssh will be allowed:

ASA(config)#ssh 0 0 OUTSIDE

NOTE : 

OUTSIDE means the outside interface where we are coming from to the ASA appliance.