A dot next to a note tells you to add half of its original duration. So a dotted half note lasts three beats (2 + 1). A dotted quarter lasts a beat and a half (1 + ½). A dotted eighth lasts three sixteenths' worth (½ + ¼). The dot is one of the most efficient symbols in music — one tiny mark replaces what would otherwise need a tie.
The most common dotted figure in drumming is the dotted-8th + 16th pair. Together they take up exactly one beat. The dotted-8th eats three of the four 16th-note slots, and the 16th gets the last slot — counted 1 (e) (&) a, with strikes on the 1 and the a. That's a long-short pair, and it's the rhythm of every march, every classic rock backbeat fill, every Sousa thump.
It's important to not confuse a dotted-8/16 with a swung 8th-note pair. They sound similar but they're different math. A swung 8th pair is built from a triplet (the long is two-thirds of a beat, the short is one-third). A dotted-8/16 is built from 16ths (the long is three-quarters of a beat, the short is one-quarter). The dotted version is tighter and snappier; the swung version is looser and rounder. Most rock and pop reads as dotted; most jazz reads as swung. The exercises below sit you firmly in the dotted/16th grid so you can tell the difference.
For the sticking, we'll use Stone-style permutations: alternating, hand-leading, and double-stop variations on the same dotted pattern. The dotted figure is so distinctive that its sticking is what colors it — the rhythm itself is fixed.