How can I estimate the required T/O power for propeller aircraft?
You need takeoff speed (from the lift coefficient, wing surface and altitude) and the time in which you need to achieve it (before you run off the runway). That'll give you the needed acceleration ($a = \frac{\Delta v}{s}$) 

From that you can know how much force the prop must generate ($F = ma$).

Add some margin to account for friction losses.