Dugtrio is really fast, but it has terrible defenses. It can often do good damage if your opponent is forced to switch, and never forget that it's known as the king of critical hits, and for good reason.
Dugtrio can make a surprisingly useful lead with this moveset. It outspeeds the fastest sleep user in Gengar, and it can severely lower Exeggutor's Sleep Powder accuracy. You could get lucky and Mimic Sleep Powder, and then put your opponent's Exeggutor to sleep. However, it is dangerous to use against a lead Jynx, as Blizzard will OHKO. Dugtrio also makes a semi-decent late-game sweeper with its high critical hit ratio and STAB Earthquake.
Dugtrio's Earthquake 3HKOes Starmie, 3HKOes Chansey, 4HKOes Tauros, and 2HKOes Alakazam on average. Earthquake only does 91% damage to Gengar, which can be annoying, but if you can get Gengar to switch in on an attack from a low-health Water-type, you can bring it down to less than 91% and then switch to Dugtrio on the expected Thunderbolt, for instance.
Slash 4HKOes Exeggutor as well, and does in the other standards in an equally quick time. Slash is the technique which, in combination with Earthquake, allows Dugtrio to do the most amount of damage to the widest range of Pokemon.
Substitute and Sand-Attack are fillers, the idea being that you Sand-Attack your opponent and try to hold on to a Substitute, and then attack from behind the Substitute. This strategy doesn't work without a fair amount of luck, but is worthy of mention.
Rock Slide works for Flying-types, but don't expect it to do much damage. Of course, Dugtrio is an excellent OHKO abuser with its Speed so Fissure works, but OHKO moves are banned most of the time. Body Slam is good if you want to paralyze something on the switch in, but it's usually better to just go for damage.
Checks and Counters
Since Dugtrio's Speed is its main asset, a paralyzing Body Slam or Stun Spore is very devastating to its cause. A single critical hit will most likely do Dugtrio in since its defenses are very low. STAB Hyper Beams, and any Pokemon with a super effective move against it will also be a capable counter. Exeggutor is a great Dugtrio counter because he can eat Dugtrio Earthquakes all day. Slowbro is also a great defensive Pokemon that can hit Dugtrio with a super effective move.