Obtaining Guild Coins
Guild Coins (sometimes called "Guild Points") can only be obtained by actively participating in Guild Battles. The number of coins you can receive after a battle depends on the amount of battle activity you logged. You will get 1 Guild Coin per 100 Battle Activity Points. Battle Activity Points are gained by using tokens in Guild Battles, either attacking other players or using support abilities like Heal and Polymorph. You will still receive activity points even if you lose a duel. Members of the winning guild will gain 25% more Guild Coins after the battle, or 35% for a "quick win" (winning by eliminating the enemy guild before the timer runs out). The losing guild will still get tokens but suffers a 25% penalty.
If you want to collect Guild Coins as efficiently as possible, take on a large guild with members on the same footing as you. Try to drag the battle as long as possible to be able to log in more activity. Use clerics and warriors and avoid mages and rogues. It's also better if the other guild is actively battling as well.
Spending Guild Coins
You spend them at the Guild Shop.
Guild Coins or Guild Points?
The image shows "Guild Points", but the in-game text usually refers to them as "Guild Coins". It doesn't really matter what they're called, it's how many you have!