You push the timer button...located on the top right of the camera (a circle with an arrow at the end), and then click the take photo button (shutter button). It will automaticly take a photo after the timer expires.
To be honest, I didn´t even know the camera had face recognition. Never used this feature... I have not used the camera for a while since I bought a Canon Sx40HS in 2012 but I agree, some of the best pictures I have ever taken was with my old good Kodak Z612. Sorry if I did not help much with my answer. Enjoy your camera !!!
I never owned the Z980 so I really cannot do a comparison - but I have had my Z990 for several years and love it. I've never had an issue with mine and even bought my sister and brother-in-law one. I would recommend the Z990 - especially if you're familiar with the Kodak Z series.