Don't have one handy, but I can explain it as best to my knowledge with the game (15 hours or so). Progression is split between two levels: Your overall player account level which is increased by your score in matches and the level of your classes - to include starfighters, heroes, and vehicles which are their own class. Each class can equip Star Cards which are modifiers to existing abilities or new abilities altogether. One Star Card may be "increase Health Boost by 10%", and another may be "Disruptor - Defuses enemy explosives that enter an area around you for 10 seconds." You can equip up to 3 cards per class at any time.
Here is where it gets tricky. To level a class you have to acquire more Star Cards. The more you have, and the higher level they are, the higher your class level will be. The Star Cards must pertain to that class to rank that class up. Heavy cards do not level Officer, for example. This is the number that you will see next to your class. If you want to unlock the card slot that needs Officer rank 10, then craft or find more Officer Star Cards. I once saw a player who was a rank 50 Assault class. In order to get that level he must have had every Assault card, and every one of those cards was upgraded to Epic (purple) quality. To obtain that so early means he easily spent over $100 on the game.
To upgrade Star Cards to the next rank, you must use a set amount of crafting parts dependent on tier, and you must be a certain overall account level. Green quality cards require account level 10, Blue 15, and Purple 20. In theory this is so people can't just find purples in lootcrates and dominate newbies (and later purples were removed from crates all together), but in reality if you find a card in a loot crate as opposed to crafting, you can equip it regardless of account level.
Lootcrates are the only way to find Star Cards. Certain challenges you can complete will reward you with special crates containing specific Cards (and will contain duplicates in my experience which is dumb), and of course you can spend credits or real money on them.