Hello Muhammad, the field inside a single coil of large diameter and small cross-section is rather inhomogeneous. The purpose of the Helmholtz coils is to have a volume of space midways between such coils in which the field is (roughly) homogeneous. In order to accomplish this the currents in both coils have to be of equal strength and direction.

For electric current and magnetic field there is a "right thread law": If you have a screw with right thread aligned parallel to the current, and you want to screw it in the direction of the current, you have to turn it with the magnetic lines. For example, if a current would flow from your head into the screen you are currently looking at, the magnetic field lines would rotate clockwise in concentric circles around the current.

In Pakistan, the magnetic earth field has components pointing down (strongest), to the north, and to the east (weakest). In order to compensate this field, your currents have to flow counter-clockwise in the pair of coils you see as circles, if you look at your system of coils in the direction of the components of the earth field, that is, down from above, from the south to the north, and from the west to the east. Hope this is helpful.

Detailed 3-axial Helmholtz coil construction is described in

Parametric design of tri-axial nested Helmholtz coils, by Jake J. Abbott

REVIEW OF SCIENTIFIC INSTRUMENTS 86, 054701 (2015), [http://dx.doi.org/10.1063/1.4919400

If you have a magnetic sensor that is sensitive enough to detect fields at a fraction of the levels that you're trying to null, the common approach is simply to use a feedback circuit to control the current until the applied fields (i.e Earth's magnetic field or other fields due to power lines, etc.) are canceled.  There are commercial systems available for this sort of active cancellation that work for oscillating fields as well as static ones.  (My company actually happens to manufacture systems like this for specific applications, which is how I know they exist!  http://ets-lindgren.com/iMagneticActiveCompensationB).