How to wire a hall effect sensor to arduino?
The UGN3503 that you use gives out a analog voltage that changes when there's a magnetic field present. So this sensor needs to be connected to an analog pin.

If there is no field present the voltage is around 2.5Volt. If the south pole of a magnetic field is present the voltage will be higher that 2.5V. With a north pole the voltage will be lower that this 2.5Volt. The amount of higher/lower voltage is based on the strength of the field.

A capacitor near the sensor could help reduce, so called, noise. Though 100µF is too high. I think you mean 100nF (0.1µF).

The pull-up is for other types of hall-effect sensors. Some of these sensors just give a HIGH of LOW output, based on whether a magnetic field is present. Those you connect to a normal input pin.