Final Fantasy 1's battle system is what sparked the battle systems for the many other games that Squaresoft have created. Similar in design to the classic final fantasy's, FF1's system incorporate a very easy learning curve and structure.
Random encounters occur when wandering the world, sailing in a ship, or rowing a canoe. They DO NOT occur while in a town, city, or otherwise established area. Random encounters can be noted by a sudden change in the screen while wandering around. The enemies you fight are compltely random, yet dependent on the area in question. If you are in a level 60+ area, you won't be fighting a level 1 enemy.
During battle, your party is pitted up against a number of enemies. Each character gets a turn for every "round" of battle. The order your characters and the enemies attack in is determined by the SPEED attribute.
When you turn comes up, you'll need an enemy to attack. Select an enemy by using the up or down arrow. In the NES version, if two characters attack the same enemy and the first one kills the enemy before the second can attack, the second will attack nothing. Plan out your attacks accordingly.
After battle is over, you'll be taken to a screen where you will receive EXP (experience points), items and gil. Experience points depend on the level of the area in question as well as your own level. Item and Gil are dependent on the monster in question.