obtaining β(hat)s from weighted least square regression

I'm doing Regression analysis under stratified random sampling for my research since it's usually assumed in many textbooks that the data is simple random sampling.. so in my case it would be stratified sampling..

How do you get the β(hat) ̂from a WLS Regression under a stratified random sample?

My professor told me to start from generating random errors, then from there we could get the β(hat).

Can someone enlighten me? Are there some theoretical explanations on this? or are there journals that i should read to help me understand more?