I must admit, I never use a GUI for Cisco gear. I am a CLI guru but it can be useful to have and is preferable for others. The issue I was having though was simple. I could not get it to work! This however was on Windows, when I tried on Linux it worked. Weird.
The config needed for using the ASDM is not hugely complex. An example is shown below:
http server enable 444 http 172.20.0.0 255.255.255.0 inside asdm image disk0:/asdm-743.bin
Enable the http server on the port specified, allow on the inside interface from the specified internal network plus include the image for the ASDM software. Easy, so why was I getting this generic error?
It turned out to be the following issue for me. I had only allowed one particular encryption cipher.
ssl server-version tlsv1-only ssl encryption aes256-sha1
All I needed to add was another cipher
ssl encryption aes256-sha1 aes128-sha1
Once added, ASDM worked like a charm. Thanks to PeteNetLive for his helpful source post.