#H_2+O_2rarrH_2O#
Notice the imbalance of atoms. On the left side, the reactant side, there are #2# hydrogen atoms and #2# oxygen atoms. On the right side, the product side, there are #2# hydrogen atoms and only #1# oxygen atom.
An important thing to remember when balancing equations is that the molecules themselves may not be changed—only their coefficients can. For example, we can change #H_2O# to #3H_2O# but we can't go from #H_2O# to #H_3O#.
In order to deal with the original imbalance, the #2# oxygens on the left and #1# on the right, we can change the coefficient of the #H_2O# molecule from #1# to #2#.
#H_2+O_2rarr2H_2O#
Now we have the same amount of oxygens on each side, #2#, but we have an unequal amount of hydrogen—there are #2# on the left and #4# on the right. We should achieve the least common multiple of the existing numbers, which is #4#. We can make the #H_2# on the left have a coefficient of #2#, giving us the #4# hydrogens that we need on that side of the equation, to match the #4# on the right.
#2H_2+O_2rarr2H_2O#
