TAPI is an API
Not sure I'm much use as I've never used anything TAPI compliant.
In general:
I guess you have checked the phones are TAPI compliant and to which version, hence the question. Are the voip phones standalone phones or are they USB phones? I'm asking because you may need to install driver onto your PC, or not.
Once that's done I guess you need to wait for someone who has used such things to assist. Or google reviews, there does seems some free software out there:
http://www.voipfone.co.uk/TAPI.phpSo is it just voice calls you need to make via a headset then? And where to, within the house, or normal POTS or where?