It is always useful to draw the Lewis structure when trying to determine if a molecule has single, double, or triple bonds.
So, ammonia (#NH_3#) has a total of #8# valence electrons, #5# from #N# and #1# from each #H# atom.
Each #H# atom bonds with the #N# in a single bond - 2 electrons shared. The 3 single bonds between #N# and the #H# atoms make up for #6# of the valence electrons, the remaining #2# being set as a lone pair around the #N# atom.
A quick way to determine the type of bonds formed is to take into account the fact that #H# can only form single bonds, since it only has one orbital filled with one electron; therefore, it only requires one electron more to form a stable doublet configuration.