Suppose a data set has increasing trend and after removing trend by 1st difference, the ACF and PACF have no any significant correlation, then how do we determine order of ARIMA(p,d,q)?
Have you look at the attached reference ? I believe this is a good start. Notably the Arima and auto.arima function from the R package forecast. The orders of your model will be determined using usual information criteria such as AIC, BIC, etc...
By the way, you do not "erase" a drift by considering 1st difference, see the reference for more details on the equations.
if after differencing the series the ACF and PACF have no significant correlation it is an indication that p=q=0 in which case the series is white noise.