How long should we charge the battery of a new mobile phone?
Dude, the new era mobiles use Li-ion and Lithium polymer batteries which don't need extended first-time charge like the old model. If you want you can charge it until it reaches 100% for the first time then just use it as you wish.
But every kind of battery has it's life cycle so if you go from 100% to 0% then charge it all the way up to 100% does more damage and reduces the life of your battery then charge it until 80% and use it until it reaches 20% the plug it back until it reaches 80%.