The mode of a data set is simply the most frequently occurring value. The mode can be determined from a stem and leaf plot using what one eminent statistician refers to as the "inter-ocular traumatic test" (i.e. by looking at it!)
For example, take the following data set:
10, 11, 20, 21, 24, 27, 27, 27, 28, 28, 29, 29, 29, 31, 33, 33, 33, 33, 33, 39, 53
1|01
2|01477788999
3|1333339
4|
5|3
Even though the peak corresponds with the 20s cohort, it's clear that the most frequently occurring value, and hence the mode, is 33.