After beating some sense into the various shop keepers scattered about the streets outside of your restaurant, you will be approached by Winston's guard. He will tell you off in pretty grand fashion, essentially telling you that he doesn't trust you and that if you make just one screw up, he'll be happy to squash you like a bug. Pleasant guy, really. He will then take Winston and wander off somewhere, leaving you alone in the streets. Luckily, there's never a lack of things to do in Sleeping Dogs, and your first Favor mission will prove this. Usually, Favors will be separate from the main storyline and will involve simple trifles between the various pedestrians standing around. But this time, since it's your first one, you will have to complete the mission in order to proceed on with the story. Luckily, it's a pretty easy one.
Look to your left to find a woman vender with a yellow speech bubble over her head. Speak with her and you will learn that she ordered a lunch from the restaurant, but hasn't paid for it yet. She will ask you to deliver the money to the restaurant in her stead. Being the sand up honest guy you are, you agree and with that you'll be off to take the money back to the restaurant. No, no matter how badly you want to, you can not steal the money for yourself. Turn to the right of the vender, facing back the way that you came from when you started the last mission, and sprint back towards the restaurant. Jump over tables and push through pedestrians to make it there faster.
When you reach the restaurant, simply run back inside through the front door and speak with the woman behind the very first counter. Explain to her that you are delivering lunch money for the vender down the street, and she will gladly accept your money. With that, your first Favor will be completed.
Most favors in the game will be just as simple as this one, although totally optional as well. You don't have to pick any of them up, but if you do, you may find yourself rewarded with extra money or experience points.