Hello Serge,
First of all, congratulations on your graduation! There is an article that will answer most of your questions:
How To Get PMP Certification - The Complete Guide
Although some of the details in the article are slightly outdated due to the most recent changes to the application requirements for the PMP and the exam structure, I recommend you also visit PMI's website where you can find the Exam Content Outline (ECO):
PMI Certification
The ECO contains more details around the eligibility requirements. You need 36 months of experience leading projects within the past 8 years. Since you are a recent grad, chances are you do not have the required experience leading projects, but I could be wrong. I encourage you to read through the requirements and assess for yourself if you qualify or not. If you don't, there's no time like the present to start working towards meeting the requirements.
All the best,