I would look into housing costs where you plan to be living, decide if you’ll be living with roommates or not, and try to save at least 6 months rent/living expenses in advance. Don’t forget to consider things like utilities/internet/gym membership in addition to food costs and the occasional glass of wine. I saved about 3-4 months, but I was very lucky to find a job as quickly as I did.
It’s impossible for me to estimate for you, since I don’t know exactly where and how you plan to be living, but it’s nothing you can’t calculate in an afternoon if you’re willing to do a little research.
I saved up by working full time and living with my mom for the better part of a year, which conveniently coincided with a dramatic dip in my social life. It’s tough, but if you’re committed to the dream, go for it! It’s not as impossible as other people like to make you think.