Soon after stepping through a large gate at the end of the street you should receive a rather enigmatic telegram from Lutece. Read the telegram, turn left and use the telescope located in Vantage Point #3 (this action is also needed to unlock the Sightseer achievement). If you'll use the telescope and point it at the lower sidewalk you'll notice the otherwise invisible Lutece pair.
Proceed towards the fair. Near the entrance to the fair (on the opposite of the vigor's presentation stand) you'll find Vantage Point #4.
The fair contains several shooting ranges. Interacting with these attractions serves as a tutorial and can also be used to gain much needed funds. Among the attractions is a vigor presentation (Bucking Bronco) situated under the "Cast the Devil Out" signboard. As for the shooting ranges, there are two of them - "Bring Down the Sky-Line Vox" and "Hunt Down the Vox". Achieving first place in each contest is awarded with 30 silver eagles, second places with 10 and third place with a pack of cigarettes.
Once you're done exploring the fair and interacting with the attractions approach a stand that offers a free sample of a vigor named Possession. Take the sample from the girl with a basket and approach an automaton which guards the entrance to the lottery. You'll learn that all the tickets have been purchased by important dignitaries, however the automaton will change its mind if you'll try the newly acquired vigor on it. There's also another stand with a free sample nearby and you can now use it to replenish your salt supplies which serve as fuel for the vigors. If you need even more salt you'll find several bottles under the canopy with the girl.
Soon after stepping through the gate you'll have a chance for your first face to face meeting with the mysterious Lutece couple. Throw a coin they gave you and head towards the lottery.
On your way to the lottery you'll also encounter two policemen. You can stop here for a moment and take a closer look at the device they have in their possession. Don't worry, because you'll soon obtain this device (after a second, more unpleasant meeting with those men).
R. Lutece monument is the next place where you should make a stop. Approach the bench and look underneath it to locate Voxophone #4.
Keep moving towards the lottery, finding a "false shepherd" poster containing a warning about the events that will soon take place. Make sure that you've explored this part of the city entirely before entering the lottery area, because you'll soon lose access to this place.