You need to rip (copy) your cds to your computer. Most people use a compressed format, such as mp3,wma, or aac. You can either use the software that comes with the Zune, Windows Media Player, or whichever music software you have. If you're not ripping with the Zune software, you'll eventually need to add the music to the Zune library. Once that's done, you connect the Zune to your computer and sync using Zune software. I would imagine that there are some sort of instructions included on how to do this.
Here's a link to "Using Windows Media Player 11." Although it's specific to WMP 11, it's pretty basic and most of the concepts can be applied to other media players and devices.
As far as paying for anything goes, you only need to pay if you are purchasing any downloaded content. You can purchase individual songs or do a monthly all you can download subscription, which is a good option if you don't have a large music library. Although once you stop paying for the subscription, you won't be able to play those songs. The songs you pay for individually are not affected by this. If you have or are planning on buying a Zune, then you'll need to use the Zune Marketplace. (It's a relationship much like iPod has with iTunes)
To get your music cd's onto the Zune, do you have to also subscribe to the pay Zune service, or can you just send them directly to the Zune? What I'm asking is what is the process?