Depending on the climate and type of grass that is growing or the type of grass you planted grass takes from 5 to 30 days to grow.
If you've just planted grass seeds you should start seeing the grass grow a little within 5 to 7 days and with proper watering the grass will usually be ready for a mowing after 30 days.
I find though that I have to mow my grass during the spring and summertime every week especially if it rains a lot.