Process after H1B selection

I (on OPT right now) have been selected for H1B. How long will it take for me to change my visa from F1 to H1B now? What are the processes that the employer has to adopt? What if I change my employer?

You can work on H1B from October 1st.
You can read Steps after H1B Lottery to understand process
You can file it as COS or Consular Processing, depending on your choice to start working. Read H1B COS vs Consular Processing