Sort the data and slice it. The p-th percentile is the value below which p% of points fall. Quartiles, deciles, and box plots are just different slicing rules.
50
Quartile rule: Q1 = 25th percentile, Q2 = median (50th), Q3 = 75th. The middle 50% — the interquartile range — is the heart of the distribution and the box of a box plot.