To reach the final boss of the game, place the remnants of the Lords of Cinder on top of their thrones in the Firelink Shrine. With this done, talk to the Fire Keeper, and then kneel by the Bonfire.
This takes you to the Flameless Shrine. Light it, and then leave the shrine. Light another Bonfire outside (the Kiln of the First Flame), and then approach the field at the top of the hill. This is where the final confrontation takes place.
The Soul of Cinder deals heavy fire and physical damage, with other damage types coming into play randomly (so you can’t really count on them). Make sure that your Resistance is high toward the big two, and start this fight.
Buffing your own weapon damage is good, but this isn’t going to be a quick skirmish. Anything that you use is going to wear off before the end of the battle, so keep your items on the hotbar, and refresh them between Stage I and Stage II.
It’s okay to train for a few runs without worrying about Embers, but once you’re really trying to win this fight, go ahead and use them. Some players like to hoard them, but this is the fight that you’re hoarding them to beat. It’s fine to lose one or two while you’re perfecting your techniques.