advice for repairing flagstone veneer front steps

by Cathy
(Toronto)

Hello
My front steps are in bad shape: several of the pieces of flagstone used as veneer have come loose and the tuckpointing has disintegrated. From what I can see, the flagstone was laid over pieces of slate and these over cement. I'm not sure if it is a poured concrete stairs underneath. I see wire netting in places, I think this holds in concrete to build up a bed to then put veneer onto. Flagstone was used on the steps and some kind of brick veneer on the risers. I have gotten various suggestions from different contractors which leaves me confused. It seems everyone agrees that the original job was done poorly, and subsequent repair work was also poor --wrong kind of cement used? Could you please advise me on what material I should use to reset the flagstone. I've read through your material and you seem to suggest Portland Cement. I had one chance to ask my dad before he recently passed away unexpectedly --he seemed to be suggesting that cement was not the right material, wouldn't have enough adhesive and I should be looking at some kind of mortar, as you would use to lay tile (but for exterior work). Any advice you could offer would be appreciated. I can't afford to hire a contractor, but am pretty handy myself, so think with right instructions I can manage the job.
many thanks
Cathy