Question:
What conditions the hardware (modem) should meet to be able to make a conference call?

Answer:
That entirely depends.  There are many different ways conference calls can be implemented:

If your telephone company provides conferencing services then you just have the modem generate any DTMF, hook flashes, etc. necessary as if you were doing it yourself from a standard og phone.

If your phone line is hooked up to a PBX that supports conferencing then it's a similar task of generating the appropriate DTMF, hook flashes, etc.

If you're using a third-party conferencing provider like Raindance, Evoke, etc. then just dial the access number for the conference call and when you hear the prompt dial the access code.

If you're not using any of the above configurations then you would need hardware that is physically capable of conferencing multiple calls together and multiple physical phone lines.  Modems typically can't do this.  To conference only two lines together you'd need something like a Dialogic voice board that provides SC Bus support.  If you want more than 2 lines then you'd need a Dialogic voice board plus a Dialogic conferencing module.  None of this comes cheap

The modem I am using is: standard modem and I am not using any calling card. may look like this: ./dial phonenumber1 phonenumber2 when the phonenumber1 answers then the phonenumber2 should get connected

by the way here in sweden if I want to do it from my phone i do the following: 1-number1 2-"when answer", I press R and a new number 3-when answer, I press R3 to join the call