The Pyra will, as shipped, run Debian Jessie, using the official Debian ARMhf repo for most software, with Pyra-specific packages available from a repo on pyra-handheld.com.
A list of software in Debian can be found here (check for armhf as the architecture).
There are beginner-friendly package-managers such as Synaptic (GUI) or gnome-packagekit. Keeping things up to date, searching for available software, and installing programs is all easily done with those. A "DBP Manager" is planned to combine installation, updating and searching for both DEB's and DBP's.
To install Debian packages on the command line, try searching for a keyword like this:
apt-cache search synthesizer. Then run
sudo apt-get install zynaddsubfx to install the program. Then type in
zynaddsubfx to run it. Try to keep your list of available software updated with
sudo apt-get update, and keep your installed programs up-to-date via
sudo apt-get upgrade. (For those new to Linux, updating can be done by the GUI explained above.)
It's important to keep your Debian software up-to-date as above, but also your DBP software as well.
If you have somehow completely borked your system, it is possible to reinstall Debian. Pyra-specific images and installer can be found here.