Use a Helmholtz coil. They are easy to construct and the actual magnetic field matches the theoretical magnetic field quite well. It is also possible to construct a three axis Helmholtz coil that would allow you to measure the hall effect at arbitrary orientations without having to move the sample for each measurement.
If you mean the ohmic contact with the wafer, you will need to consider the wafer details (doping type, etc...) as well as the processing just before deposition of the ZnO. Any native oxide on the wafer will render that contact non-ohmic.
If you are referring to a contact that you make on top, you will need to consider the details about what contact metal you are using and how it is deposited on the surface. It is typical to use Ti/Al or ITO on ZnO to make ohmic contacts.
For a simple electrical contact, this group reported that they were able to achieve high quality ohmic contacts with ZnO using Ti/Al. Low-Resistance Ti/Al Ohmic Contact on Undoped ZnO, Journal of Electronic Materials, Vol. 31, No. 8, 2002.
Since this is a quite complicated subject and you may want something other than a simple electrical contact, you may want to read ZnO Schottky barriers and Ohmic contacts, J. Appl. Phys. 109, 121301 (2011); http://dx.doi.org/10.1063/1.3581173
In the end, you will need to make the measurements yourself since your process parameters will effect the quality of the ohmic contact. You should use the transmission line measurement method which will also allow you to calculate your sheet resistance if you do it with varying lengths between contacts. You may also use a four point probe but I believe you can better characterize your films and junctions with the former.
Thank you so much for you advice. I have found that Al has widely been used as ohmic contact for ZnO by soldering method. I will try to apply and see hoe reliable data I can get. If you have any suggestion, feel free to let me know.