Once you have an address (at least a semi-permanent one), you need to request the Residence Permit at the city’s migration office, the “Office Cantonal de la Population et des Migrations” (better known as OCPM). Note that if you are living outside the canton of Geneva, the residence permit should be requested in your corresponding place of residence.
For detailed information regarding Swiss residence permits, please refer to the official Graduate Institute pages.
Since it is a busy period of time for the OCPM, we recommend you do it as soon as possible. Gather all the documents requested, the fee money, your headphones, a good book and maybe a snack, and be prepared for a long waiting time in a busy waiting room.
Your residence permit card will be mailed to you after some weeks to the address you presented.
Remember that if you move and change address later on, you will need to inform the OCPM by presenting a form and paying the fee.