Firstly, the only way to level beyond lvl 20 is with Armour with light levels. If you look at the items that give you light, it will have a +10 for example. It can be a lower or higher light level for each item. Just equip the highest level item you have, if a new item is not better then just salvage it. You also get a higher light level by upgrading these armour items. There is a yellow bar on the bottom of your emblem that shows how much light you have, and how much more you need to get to the next level.
You can get these items in several different ways. The simplest way to lvl up when you first hit 20 is to get a blue armour engram item. If your lvl 20 or higher it will always have a + light level attached to it. You can get blue engrams pretty much anywhere in the game. If your playing against the AI or PVE as they call it, it can just randomly drop for an enemy being killed. You don’t necessarily have to kill them yourself. It can be killed by someone in your fire team, or just a random person. It also doesn’t matter if your killing a lvl 2 or lvl 20 enemy, the drop will be in according to your current level. In multiplayer/ Crucible you can roll an item at the end of each game. It really doesn’t matter how well you played. It just seems to be random most the time.
If you just hit lvl 20 and want to get light levels fast. It’s a good idea to just farm for them. There is a spot on Venus that I find is the best place. Here is a link to a video of where exactly it is. https://www.youtube.com/watch?v=cmMaZEIV8hI Doing it this way is a pretty fast way to get to lvl 24/25, but to get higher then that you really need to be lucky with random drops. I will add also decrypting engrams with the Cryptarch gets you leveling points for the Cryptach. As you get higher levels with him he will give you some good gifts that you receive in your mailbox like blue light level amour amongst other stuff.
If your lucky you will get Legendary Purple items drop or roll for you that give you much higher Light levels, also weapons that are very powerful
The surefire way to go beyond lvl 24/25 is to buy the amour from either the Crucible Master, Vanguard Master or a Faction Master. These items are all Legendary/Purple. To join a faction you just need to buy a cape from them and you will now be part of that faction. Don’t worry you are not locked in or sacrificing anything by doing this. But if you do decide to change factions you will need to start leveling up from the beginning again with them. Here is a guide on witch one you should choose.
The Faction combinations are as follows:
Dead Orbit: DIS/STR
Future War Cult: INT/DIS
Intellect: Intellect decreases the cool down time of your Super, allowing you to use it more often.
Discipline: Discipline decreases the cool down time of your grenades, allowing you to use them more often.
Strength: Strength reduces the cool down time of your melee modifier, allowing you to use it more often.
How it works is, all the reputation points you earn after joining the faction are added up for that faction, whether it be Vanguard rep or Cruicible rep. But you still have the rep for the other 2 as well. So you can choose which one to buy your items from when you have the right amount of rep and marks.
Rep is separate to marks. When you hover over the mission or crucible evet you want to play, it will show you what you can earn from it. The rep can be earned by just grinding as much as you want. But the marks are limited to 100 of each per week per player. 100 Vanguard and 100 Crucible. But to hit the 100 mark in the week you are either playing for many hours or just a legend at multiplayer.
You also get rep and marks from doing bounties, so be sure to check what bounties are available, and get the ones you think you can achieve. They bounties available change from day to day. So keep checking them to find the ones that are easier to finish.
In the game you will on occasions find Strange Coins and Mote of Lights. Make sure you keep these. On the weekends a merchant called Xur will appear at the Tower near the Crucible vendors where you can exchange these for Orange Exotic items. These are the highest lvl items you can acquire in the game.