The CM team was originally shooting for last week to get the first CyanogenMod 12.1 nightlies out the door, but they're just rolling out now. This process will take a little time as the new version hits the myriad of devices supported by CM these days. When it does show up, just remember that we're talking about nightly builds, so don't expect a bug-free experience.
CyanogenMod 12.1 is based on Android 5.1, which is still rolling out to Nexus devices. The new version will install on top of CM 12, but any third-party add-on ZIPs (read: Gapps) need to be updated manually. That means finding a version compatible with Android 5.1.
So far, CM 12.1 is live for the devices like the OnePlus One, Moto G, 2013 LTE Nexus 7, and Moto E. CM 12.1 nightlies will continue appearing throughout the day, and every day henceforth until there's a new version or the sun burns out. A milestone build will pop up eventually, which should be more stable, if you want to wait for that.
- CyanogenMod Downloads