On the ASA you will need to create network and or host objects for both networks (192.168.1.0/24 and 192.168.2.0.24) or individual devices.
You will then need to create access rules. The easiest, but most insecure, way is to just create a rule on Eth0\0 for source 192.168.2.0\24 destination 192.168.1.0\24 service ip action permit and a rule on Eth0\1 for source 192.168.1.0\24 destination 192.168.2.0\24 service ip action permit.
The better way is to determine what each device or network needs access to and only allow create rules for that traffic. For example, if devices on network 192.168.2.0\24 only need access to the email server at 192.168.1.3 using imap then the rule would be something similar to this. On interface Eth0\0 create a rule for source 192.168.2.0\24 destination 192.168.1.3\32 service tcp\143,tcp993 action permit.
If devices on network 192.168.1.0\24 only need access to the web server at 192.168.2.3 using https then the rule would be similar to this. On interface Eth0\1 create a rule for source 192.168.1.1\24 destination 192.168.2.3 service tcp\443 action permit.
Unless you are very familiar with creating Cisco ASA configs using the command line, I would highly recommend using the Cisco ASDM app to access the ASA. This will give you a GUI for configuring the ASA. It is usually easier to create objects (ie network object, network groups, service objects, service groups) and use those in your rules. Most well known services (ie http, https, ssh) should already have predefined service objects in ASDM to use in your rules.
I hope that helped. Good luck.
Jeff
