The Destiny 2 On Your Laurels Exotic quest is one of the main objectives attached to the 2020 Guardian Games event, and it's got some of the best rewards: three exclusive Exotic Ghost shells themed after Titans, Hunters, and Warlocks. You can earn one Exotic Ghost shell each week, so if you complete the quest for all three weeks that the Guardian Games is around, you can add all three to your collection.
To complete this quest, you need to collect a certain amount of laurels each week. So, how do you get laurels? Well, laurels are new collectibles which drop from enemies defeated by abilities - Supers, grenades, and charged melee abilities. Enemies in all activities drop laurels, and if your teammates get kills with abilities, those kills will spawn laurels as well. Laurels disappear about 10 seconds after they drop, so be sure to grab them quickly.
Note that laurels are class specific - if you're a Hunter, you'll generate Hunter laurels, and so on. Additionally, laurels which match the class you're playing are worth three points of quest progress while other laurels are only worth one point. So if I'm a Titan doing a strike with a Titan and a Warlock, my Titan buddy will spawn laurels worth three points for me, while my Warlock's laurels will only be worth one point for me. This encourages players to clear activities with fireteams of the same class so everyone gains more quest progress.
To speed up your laurel farming even further, use a build that lets you spam abilities, especially grenades and melees since they're more accessible than supers. Titans can use An Insurmountable Skullfort to spam charged melee abilities, Warlocks can use Devour and Nezarec's Sin to increase uptime on all their abilities, and Hunters can melee indefinitely by using Gambler's Dodge with top-tree Arcstrider. That's to say nothing of Ophidia Spathe, Heart of Inmost Light, Crown of Tempests, and plenty of other ability-boosting Exotics. Use whatever you're comfortable with, as long as it helps your abilities.
Here's how to clear the Destiny 2 Void Feast bounty.