As you've probably worked out, the key to levelling up quickly in Destiny is to focus on a few specific things and to do as many things at once as possible. One of the best places to do this is on Patrol, where you collect missions from blinking green beacons scattered around the map, complete Public Events and bounties, and locate materials that you can use to upgrade weapons and armour. You can launch a Patrol on each of the four planets that ship with the game, and there are a few things worth memorising in each setting.
Where to find Majors and Ultras on Patrol
One of the most common and easy-to-complete bounties is to take down 10 Majors or Ultras from one of the game's enemy races. There are story missions where you can do this a lot faster (the Sword of Crota for Hive Ultras, The Archive on Heroic for Fallen), but there are also a few spots on each map that you can access through Patrol missions where you will be able to complete these bounties fairly quickly and without much effort.
Earth / Cosmodrome Majors and Ultras locations
Hive - The Cosmodrome is the best place to complete the Hive bounty by far and it will take very little time. Straight ahead of where you spawn at The Steppes is a rusty shack with a staircase leading down. Follow it and you will find yourself in a dark tunnel. Go right and then right again into the first room you find and you should see a Hive Knight and two Hive Acolytes, all with those precious yellow health bars. Take them down and then retreat out of the room and go to either end of the tunnel and wait a few seconds. Return to the room and the Knight and Acolytes should have respawned so you can kill them again. Sometimes they take a little longer, but at most it should take you 5-10 minutes to complete the bounty.
Fallen - From the Steppes spawn point, do a 180 and head to The Divide, which you reach by exiting through the battle-worn building at the end of the area. Once in The Divide, head over to the right, past the buildings to the open area with a rusting tank. Fallen dropships appear overhead at regular intervals and one of them always deposits a group of four Fallen Vandals, one of whom has the telltale yellow health bar. Kill him, do a lap of the area to gather materials and collect beacon missions, and by the time you return his replacement should have arrived for another killing. It shouldn't take more than 10-15 minutes to do this the required 10 times. If this gets boring, you could also head through to the Rocketyard from here (it's on the other side from the Steppes entrypoint) and head to the far back corner where the Servitor and Dregs usually reside. Every so often there are three yellow-bar Fallen Vandals instead.
Moon Majors and Ultras locations
Hive - If you can spare the time, you are better off doing the Sword of Crota mission a couple of times to fulfil this bounty, but if you are happy to be more leisurely about things then there are a couple of places you can visit to find Majors and Ultras. Straight up the hill from the Archer's Line spawn and through the domed building on the right is one of the entrances to the Moon interior, and this is usually protected by a pair of yellow-health-bar-toting Hive Knights. Alternatively, if you descend into the heart of the planet and visit the Circle of Bones area - pretty much all roads lead here eventually - there are a pair of higher-level Hive Knights at one end of the path that circles the Hellmouth, the one that leads to the boss fight entrance in the Summoning Pits Strike.
Fallen - Again, you are better off trying to find Fallen Majors and Ultras during story missions, but if you are doing laps of the Moon then do call in on the old accelerator building near the spawn in the Archer's Line area - the place where you went first of all when you arrived at the Moon in a story mission. There's usually a high-ranking Fallen Vandal inside along with low-level goons. You also encounter Fallen Majors in various other locations at different times, including around the cracked dome on top of the hill in the middle of Archer's Line.
Venus Majors and Ultras locations
Fallen - There are a couple of good spots on Venus for farming Fallen Majors and Ultras. One is on Ishtar Cliffs, the area you reach by following the Shattered Coast path, where a Fallen dropship frequently deposits yellow-bar Vandals and you can also find one in the dark swampy area away from the cliff edge, guarded by a trio of Shanks. The other location is Ember Caves - reached by going left from the spawn then taking the right fork when you come out into the open again - where a Fallen Captain repeatedly spawns on the raised platform on the left of the area in front of a cave leading to The Cinders.
Vex - Playing story missions on higher difficulty will generally yield plenty of Vex enemies with those all-important yellow health bars, but if you're desperate to do it on Patrol, try The Citadel, which is reached by going left from the Patrol spawn, then taking the right exit after you enter the Ember Caves area. Once in The Citadel, go under the bridge and head left, then climb the steps and you should encounter some Minotaurs, one of whom has a yellow health bar. Once they are down, some Major Goblins will attack you from the left just for good measure. By the time they're down, the Minotaurs should have respawned.
Mars Majors and Ultras locations
Cabal - Perhaps one reason the Cabal have a stranglehold on Mars is that their highest-ranking figures aren't seen in public in conveniently killable groups. That won't stop you finishing this bounty fairly quickly though. From the Patrol spawn, head through the tunnel on the far left of The Barrens into The Hollows, then simply go into the left entrance of the first building you encounter - the one at the base of the skyscraper on your left - and you will find an Imperial Phalanx with a yellow health bar. Kill him, exit the building, do a lap of the area and when you return he will be waiting for you to kill him again. And again. And again.
Farming Spinmetal, Helium Filaments, Spirit Bloom and Relic Iron
Once you get deep enough into Destiny's gear grind, you are going to start needing large quantities of planetary materials in order to max out the upgrade trees for your weapons and armour. The good news is that planetary materials are abundant on all four of the game's shipping environments: Spinmetal is on Earth, Helium Filaments are on the Moon, Spirit Bloom is on Venus and Relic Iron is on Mars. The bad news is that their positions rotate and they only reappear a little while after players have claimed them, so it can take a while to gather the things you need.
There are various video guides available on YouTube that can help you optimise your route through each planet's many regions to harvest the most materials. However, if you want our advice, you will have more fun just buddying up with a friend and taking a disorganised approach. Combining mat-farming with Public Event grinding is a good way to keep things interesting: load up the event timer and move to an area where an event is imminent, then kill time by checking in every cave you see, looking behind things and on elevated areas - such as the grassy spires in the Ishtar Cliffs region of Venus - and highlighting finds for each other. You're not just looking for mineral deposits - every loot cache chest you find will contain a bit of material as well.
One thing to bear in mind though: once they are first claimed, there is a short window of time for other players in the vicinity to pick up the same material or access the same open chest, so it is good etiquette to point any discoveries out to fireteam companions or, if you're cruising around in the company of a few randoms, maybe giving a wave to signal your find.