When you complete the first level (1-1), there's an option to go back to the Nexus (hub). When you then go back to the same archstone that you went to to get to 1-1, you'll see the next level has appeared. That's 1-2.|
And if you choose the 2nd archstone from the nexus to select the available level (2-1), once you've done that and come back, you'll see the next one available (2-2)
Other tips include tendency. Both character tendency and world tendency. Which are affected by various things. I'd highly recommend reading up on the wiki about tendency - it doesn't spoil that much and can help you avoid messing a few things up
For reference - the more 'good' things you do, the whiter things get. The whiter the world, the easier the monsters are, but the lower the drop rate for items.
The more 'bad' things you do, it's reversed - harder monsters but better loot.
In addition, at pure white and pure black, different things can happen. Certain NPC's appear, or disappear, some gates are open, or no longer open etc etc.
If you want to keep your tendency as it is, it is *highly* recommended that you suicide in the nexus if you are in body form. You get your body form back by killing bosses and using stones of ephemeral eyes. Think hollow/unhollow in dark souls
The reason you should do this, is because if you die in human form in a world, it pushes the tendency towards black. Fine if you're after that, but I'd read up on it beforehand to decide what you want to do.
So when you kill a boss, you will automatically get your body form back. Most people at this point go to the nexus and kill themselves because that doesn't affect the tendency (there's no world tendency events in the nexus).
It's a bit weird, but once you get used to it, you'll be fine
Don't forget you can do any world's first level in any order. So 1-1, and then if you wanted to, say, you could then go to 4-1 for example.
Some people follow a sort of 'route' through the levels, once they find items that would suit their character style in certain worlds.