Hi, I’ve lived in SF for the past 4 years or so. When I first moved here I was making very little money. It’s an expensive city but it’s worth it—so much fun, so much to do, so many amazing creative people. The most expensive thing by far is the rent, but if you are willing to share with a lot of roommates, it’s slightly better.
Be prepared to spend $800/month on rent. There are still some places where you can find rent in a shared place for as little as $600, but they are very hard to find. The good news is that SF is all rent-controled, so if you find a place you can afford, the price will never go up more than 2% a year!
Food you can actually do on-the-cheap, if you’re willing to prepare your own food and not eat out all the time, or eat lots of burritos which only cost $4 and keep you full for hours. And for the times when you do want to eat out, there are plenty of cheap places in the Mission. Entertainment is inexpensive, compared to other big cities—you can hit the bars in the mission for live music and a cover under $10. You won’t be able to keep a car in the city, unless you make a lot of money to pay for a parking spot, but most young people here get around on bikes or public transit (an unlimited bus/train pass within SF is only $45 a month.
Overall, you’d want to budget $1500 a month. I have friends who have gotten by on less, close to $1200, but they were definitely living hand-to-mouth and definitely not going out for beers a lot. The thing is, there are so many great outdoorsy things to do, you can find entertainment without spending lots of money.
Hope this helps!