People use different grips, and in returning, the choice of grip, should be the one that is most effective for you. There is no "standard" answer. Most people, however, return with their normal groundstroking grip- whatever that may be.
The most important thing in returning a hard/flat serve is to, first, get your racket on the ball, and second, get it over the net, deep enough, and/or placed well enough that it causes the opponent some distress.
A hard/flat serve is normally an attempt at an ace- so they are hitting the ball (if they can) beyond your reach. So the main thing for you to do is 1) give yourself room to react to the ball/serve. Take a step back if necessary. 2) Watch thir racket strike the ball and determine where it is going- left or right- or right at you. 3) Crouch down, since the bounce will be low, get down there where the ball is. 4) Have tension in your legs. Be ready to push off/turn/step into the ball. 5) If it is really a fast ball, you do not have time for a big, full stoke. Keep your stroke simple- much of your work (as far as powering the ball back) will be done for you with the server supplying the pace. 6) Have some idea of what you want to do with the ball as you are sending it back- depth, down the line, crosscourt, spin.
But, first, get your racket on the ball, if not, all the rest, well, becomes pointless.