How does a transformer increase voltage while decreasing the current?
Ohmls Law states V = IR. That means when we increase voltage we must also increase the current (I).


That is true when feeding a resistor.


  But transformer increases the current while decreasing the voltage or decreasing the current while increasing the voltage.


A transformer is not a resistor so you can't use Ohm's law on it.


  How does it happen?


A transformer is an electrical gearbox.

        | In                      | Out
--------+-------------------------+-------------------------
Gearbox | High speed, low torque. | Low speed, high torque.
Trafo   | High V, low I           | Low V, high I


It's important to realise that (ignoring losses) power in = power out. From the Joule-Lenz Law we know that P = VI so if V is reduced I must increase inversely.