There are various ways to advance your character in Star Conflict.
There are several currencies in the game that can be used to purchase ships and equipment: Credits, Galactic Standards, Loyalty Vouchers and Artifacts.
Credits are the main in-game currency, and are earned through combat. PvP will give some credits, and PvE will give a lot. Credits are used to buy non-Premium ships. They are also used to buy mk 1 and mk 2 equipment. Credits can also be purchased with Galactic Standards.
Galactic Standards (GS) are purchased with real life money. They are used to buy Premium ships and upgrade equipment to mk 3.
Loyalty vouchers are earned by completing contracts for your chosen subfaction. Loyalty vouchers are used to upgrade equipment to mk 3, but the vouchers must be of the right faction for the piece of equipment.
Artifacts are earned by looting. When you find a purple upgrade kit, you can choose to salvage it for artifacts (you receive a small number if you salvage it yourself, or more if you pay GS). You can also sometimes find artifacts themselves as loot. Artifacts are used to upgrade equipment to the most powerful level - mk 4.
Ships and Synergy
The main type of advancement through the game is buying and upgrading ships. Non-Premium ships (or "Credit ships") are bought with Credits. Before you can buy a ship you must earn enough synergy with one of its prerequisite ships to unlock it. Premium ships are bought with Galactic Standards and do not require a specific prerequisite, though you can only buy Premium ships up to 3 ranks higher than the highest rank ship you currently own.
Once you own a ship, you can upgrade it by earning Synergy. Synergy is a measure of your proficiency in a particular ship. By flying a ship you will earn synergy points for that ship. When you gain enough synergy points, you can spend it in the ship fitting screen to level up that ship. In addition to synergy with a particular ship you will also earn a small amount of "free" synergy, that can be used to level up any ship.
The higher your level in a ship, the better it will perform, gaining a small increase in statistics across the board and some bonuses. Once you gain maximum synergy level in a ship the spare synergy can be transferred to another ship by paying Galactic Standards.
Rank is gained with factions by buying their ships. Your rank with each faction is simply the highest rank ship you own of theirs. The higher your rank with a faction, the more contracts their subfactions will offer you. Gaining rank also unlocks new implants.
Equipment is initially bought at mk 1 with credits. Mk 1 equipment can be upgraded to mk 2 either with credits or by using a mk 2 upgrade kit, which can sometimes be found when looting. Mk 2 equipment can be upgraded to mk 3 either by paying the right type of loyalty vouchers, or by paying Galactic Standards. Mk 3 equipment can be upgraded to mk 4 either by spending Artifacts, which are found by looting, or by using a mk 4 upgrade kit, which are also only found from looting.