Well I don't have much time (have a test to study for and it's late), but here is the basic instruction:
In Axon's web interface, first create or edit an extension in Axon for your PAP2. Axon comes with a bunch of default extensions you can get rid of if you want. You can also choose to use one of the default ones or create a new one. Either way just so long as you note down and set a password for one of the extensions you should be good to go.
Next go to External Lines and create a new external line for each SIP account you have (you may want to delete the default lines that come with Axon if you don't plan on using them).
For each external line you'll be able to enter the required username, password and server address for each VoIP provider. Set each external line to ring to the extension you just set-up.
The next step is to login to your PAP2's web interface. The basic minimal settings to change are the username, password and proxy/server. The username should be the extension you setup in Axon (e.g. 101), the password should be the password for the extension, and the proxy/server/domain should be the IP address of the PC running Axon.
*P.S. If you don't know your PAP2's IP address to access it's web interface, I believe you can get it by dialing **** rapidly on the phone connected to it (even if there is no dialtone) and it should present you with a menu. If I remember correctly, option 110# is for retrieving the IP address. If all else fails, you can use your router's DHCP table (if it has one) to try and figure out the IP that way.
After you submit, the PAP 2 should register with Axon, and your PAP2's status page should show this. You should also get a dial tone now.
The last step is to configure your dial plan. Go back to Axon and edit the default dial-plan. Set the default line to use (at bottom) to your default line (i.e. betamax). Then create a rule such that when you dial x as a prefix, it removes the x digit(s) and sends the call out on the vbuzzer line.
*Note: You probably do not want to use # to separate your dialling as for many ATAs (including the PAP2 I think) dialling # immediately aborts dialling. Instead use an uncommon prefix or an unused area code to differentiate them. E.g. in North America you can set the prefix to 00 since there are no numbers that start with those digits, in Australia I think 1 would do.