I am using 2 array crossed yagi-uda antenna operating at 437.025 MHz. Where and how should I ground it? Should I ground at mast of antenna or to its metallic boom?
A Yagi-Uda antenna is a dipole antenna (sometimes folded dipole) with extra parasitic elements. Both the dipole and the parasitic elements are symmetrical; therefore the antenna is balanced; therefore it does not require any connection to ground to perform as designed.
You may wish to use grounding for protection against lightning or electrostatic buildup, but those are independent of the antenna design and can be done away from the antenna itself. (Lightning protection is a complex topic and must consider the electrical connections and physical layout in the whole station and building.)