With the down payment certificate and contract, ID card and real estate license, you can apply for a mortgage loan at the bank (all commercial banks can) and entrust the bank to handle the formalities of property right transfer. The bank will inform you of the relevant expenses needed, and it is best to determine the loan term and monthly payment.
If you pay in one lump sum, the procedure is simple. However, there are many specific matters of second-hand housing mortgage loans, and it will be harder without an intermediary!