The Legend of Dragoon/Seles

After the cutscenes, go down and press psx: X at the fence to jump over it. You'll come across two soldiers who will eventually fight you. Don't worry, this fight is impossible to lose. They'll throw knives which deal 1 damage, or a sword slash which does 3. There is no need to use healing potions or attack items, so just attack them with your double slash. After you've beaten them, open the chest near the fence to get a BurnOut, which is an attack item, then exit the screen.

Boss: Commander
After some talking with him, you'll fight your first boss. It's a Commander who is accompanied by two minor soldiers. The Commander has just 20 HP while the soldiers have 5 HP. Try finishing your addition to hit a 6. If you kill the commander before the soldiers, they'll just run away. The commander has one healing potion which he'll use, you should too if you're low on health. If you want to, use the BurnOut on the Commander to do some damage. If you kill his soldiers he'll grow in power, causing him to inflict 6 damage instead of 3. He also has a BurnOut that he may use on you, which will inflict 9 damage. Just attack him with your double slash until he dies. Eventually they'll go down and you'll level up and receive a new addition, Volcano, along with a BurnOut and two healing potions.

Exiting Seles
Now that you're level two you'll have 60 HP instead of 30 and your attack will be stronger. You can go to your menu by pressing psx: Start and then change your additions if you want to select Volcano. You're now free to wander around the village. Go to the upper-right screen to find a cemetery. Keep pressing psx: X near every tombstone until you find a Stardust. Stardusts can be traded with a merchant which you'll meet later for items. Near the exit you'll see a man with a cape, talk to him if you need a tutorial about additions. After you're done exit the screen.