What are the different currencies and how are they earned?

From the official wiki:

• Coin is the most common form of currency accepted by NPCs and is the basis for player trade. It can be obtained via loot or as rewards for completing events or completing achievements.
• Gems are used to purchase items from the in-game store; they can be exchanged or traded for coin.
• Glory is used to unlock skins for use in Structured PvP; it can only be obtained through participation in that game mode.
• Influence can be spent on guild upgrades and boons; it is earned when players representing a guild participate in events, PvP, personal storyline. A guild's accumulated influence can be seen via the guild panel (G).
• Karma is used to purchase special items from designated NPCs; it cannot be traded and must be earned by participating in dynamic events, helping others with their personal storylines, or completing dungeons.
• Skill points are used to unlock new skills and Miyani will take them in exchange for mystic items or recipes.
• Supply is acquired through and used in WvW to build structure upgrades and siege weapons.
• Tokens are earned by completing dungeons. Dungeon Merchants will accept them in exchange for items unique to that dungeon.

As you stated, gold/silver/copper is the standard generic currency. It is used to buy/sell things on the auction house, repair item, buy gems, & buy things from general merchants. It is earned by killing stuff, selling monster drops, quests, opening loot bags, & from events.

Gems are the premium real money currency. It can be bought with either real money or with gold/silver/copper. It is used to buy cosmetic items and to upgrade some account/character features. It is not a 'pay to win' currency. If anything it is a 'pay for convenience' currency.

Karma is awarded by completed events and quests. It is spent at karma vendors. Theses are special shops that sell some specific items (crafting materials and magic items) and only take karma as currency.

There are also some other forms of currency whos, names are currently escaping me. One that is rewarded as part of PvP and one that is rewarded from kills in WvW. Each of them are used inside of shops within their respective zones.