First of all, there are two methods (as usually): root and non-root method. Root method obviously requires the root access to work but you can combine the root and non-root method to reach the better result.
By charging your phone means, that the battery is recieving some power. There are a few things that affect the charging time. First of all, it's the size of the voltage - you can check the voltage if you remove the back cover of your phone and look on the battery. Now we're getting to the root method - the fast charge method by recieving more juice to the battery. This method, however, doesn't only require root access but also custom kernel that supports the fast charge.
If you have the fast-charge kernel support, download this app. Simply connect your phone to your charger and enable the fast charge to take the effect.
Now we're getting to another method. Most of the newer devices are using USB2.0 or even USB3.0. These ports provide much faster data transfer and/therefore giving to your phone more juice.
Needless to say, if you use your phone while charging, the battery charge time will be much longer.a
So, if you want to charge your phone faster without root, you can use this method -
- Don't use charger, connect your smartphone to the USB2.0/3.0 port using proper cable.
- If you use charger, use the AC Charger.
- While charging, turn your phone OFF!
- If you don't want to turn your phone off, turn on the airplane mode.
You might also want to know, the newer Qualcomm processors are using the amazing feature quick charge, which is built-in on some devices like Google Nexus 4, Nexus 7 2013 and on all devices using Snapdragon S4 Pro.
There's also the feature quick charge 2, which is supposedly much more effective than the quick charge (1) and should be built-in on devices using Snapdragon 800.
Here's for comparsion:
More about quick charge can be found here.