HOW CAN WE DETERMINE THE REACTION …

Along with the below answer you can sometimes just easily determine the order of reaction just by the unit/dimension of the rate of reaction. 

ZERO ORDER:
<font size="+2">rate = k[A]⁰</font> 
<font size="+2"> M/t = k</font> 

<font size="+2">K units:  M/s, M/min, M/hr, etc.</font>

FIRST ORDER: 
<font size="+2">rate =K[A]</font> 
<font size="+2"> M/t =K M</font> 
<font size="+2">  Kunits: s^-1, min^-1, hr^-1, etc.</font>

SECOND ORDER:
<font size="+2">rate =K[A]²      rate =K[A][B]</font> 
<font size="+2"> M/t =KM²</font> 

<font size="+2">Kunits: M^-1s^-1, M^-1min^-1, M^-1hr^-1, etc.</font>

THIRD ORDER: 
<font size="+2">rate =K[A]³      rate =K[A]²[B]     rate =K[A][B][C]</font> 
<font size="+2"> M/t =K M³</font> 

<font size="+2">Kunits: M^-2s^-1, M^-2min^-1, M^-2hr^-1, etc.</font>

N ORDER: 
<font size="+2">rate =K[A]ⁿ</font> 
<font size="+2"> M/t =K Mⁿ</font> 

<font size="+2">Kunits: M^-(n-1)s^-1</font>

Ans. The order of a chemical reaction is defined as the sum of the powers of the concentration of the reactants in the rate equation of that particular chemical reaction. A reaction can also have a reaction order with respect to a reactant if the rate is not simply proportional to some power of the concentration of that reactant.

Consider a general reaction:

$aA + bB \to cC + dD$

The rate expression for this reaction is (say) :  $-r_a = k{A}^x{B}^y$

Here,  x and y indicate how sensitive the rate is to the change in concentration of A and B.

Hence, the order of this reaction is (x + y).

Note that the x and y may not respectively correspond to the stoichiometric coefficients of A and B.