To request your residency permit (permiso de residencia) in Mexico as a foreigner, you typically need to follow these steps:

1. Determine your visa type: Before applying for a residency permit, ensure you have the appropriate visa type that allows for residency in Mexico. This could be a temporary or permanent resident visa, depending on your situation (e.g., work, family reunification, retirement, etc.).

2. Prepare required documents: Gather all necessary documents required for your specific residency application. These may include your passport, visa, proof of financial means, proof of address in Mexico, application forms, and any additional documents depending on your visa category. Ensure you have all of these and your personal documents translated into Spanish (if they are in a language other than Spanish) with a mexican sworn translator for them to be accepted by the corresponding authorities.

3. Schedule an appointment: Depending on where you’re applying, you may need to schedule an appointment at the nearest immigration office (Instituto Nacional de Migración, INM) or the Mexican consulate or embassy abroad. Check their website or contact them directly to find out their specific procedures for scheduling appointments.

4. Attend the appointment: On the day of your appointment, bring all required documents and submit your application to the immigration authorities. You may also need to provide biometric data (fingerprints, photograph) during the appointment.

5. Pay fees: There are typically fees associated with residency permit applications. Make sure to inquire about the current fee schedule and pay the required amount during your appointment.

6. Wait for processing: After submitting your application, you’ll need to wait for it to be processed. Processing times can vary depending on the workload of the immigration office and your specific circumstances.

7. Receive your residency permit: Once your application is approved, you’ll be issued a residency permit (usually in the form of a card) that allows you to legally reside in Mexico according to the terms of your visa.

8. Renewal: Remember that residency permits have expiration dates, so be sure to renew your permit before it expires if you plan to continue living in Mexico.

It’s important to consult official sources such as the Instituto Nacional de Migración (INM) or the Mexican consulate/embassy in your country for the most accurate and up-to-date information regarding the residency application process and requirements.