The member making the transfer just needs to call MS and instruct them to transfer X number of points to *your name*, *your address* and MS will do the rest. Some have done this with a 3-way call so you can hear that the transfer has been completed. Some have indicated that MS will need your member number, but that was not always the case and I'm not convinced it is necessary since MS was able to find your account using your name and city of residence. Regardless, it is possible that the member number may be required at this time. As the receiving member, you really have no part in the process.
The transfer is completed manually, so it may take a couple of days before the points are in your account and available for use.
Good luck!