Calculating pH and poH of acidic solutions

Feb 2018
Calculate the pH when 1 molar of HCl acid dissociates in water?
In this question, most books solve it by taking the concentration of H as 1 molar and the PH will come out to be 0 and the POH is 14, but we know that water also ionizes itself giving out H+ and OH- So there isn't only 1 molar of H because not only HCl but water also ionizes to give some H+, but while calculating OH concentration we consider OH- ions which ionized from water - why is this so?
And do we also neglect H+ ions of water while calculating weak acid pH?