I've been to several bonfires, and I can't seem to level up. Now I'm too afraid to go anywhere and die, because I have 2,500 souls and don't want to lose them. I'm assuming there's some new mechanic in Dark Souls II where you can't just level up at any bonfire. Help!
You won't be able to level up at all until you get past the Things Betwixt area -- essentially, the tutorial. Past that and through a narrow cave is a town called Majula.
When you first enter Majula, there is an area to the right which has a tall tower overlooking the sea. To the right of that, slightly down the cliff and by a tree, there is a green-cloaked woman known as the Emerald Herald. Once you speak to her, she will relocate to the Majula bonfire. Thereafter, you can speak to her and level up at that bonfire. Unlike Dark Souls, this is the only place you can spend souls to level up.
When speaking to her at the Majula bonfire, be sure to wait for a menu to popup. You may have to speak to her several times before the option becomes available.
As a side piece of advice, if you want to save your souls until you can first spend them, don't go down into the area with the two trolls. This is a difficult encounter for a new character. You can bypass that and come back to it later to fight them.