First of all, Dino is written in C++ so you need to have a C++ compiler installed.

Dino uses a number of external libraries to handle things like GUI widgets, MIDI events, and transport synchronisation. This means that you will need to have these libraries installed on your system in order to use Dino. Your Linux distribution probably has packages for all these libraries, so look there before you download anything from their webpages. The required libraries are

libjack This is the JACK library and daemon and if you have used Linux audio software before you probably have this already. Dino uses it to send MIDI data and to synchronise with other JACK clients. You will need to run the jackd daemon for the Dino sequencer to work, but you will be able to edit songs without it. The daemon will be started automatically when needed if you set the environment variable JACK_START_SERVER to 1.

Dino requires a version of JACK that works with MIDI as well as audio. You will need at least version 0.102.6 (which unfortunately is only available in public CVS so far).
libglademm This is used to load UI definition files and connect the UI to the program logic. It requires a whole set of other libraries that Dino also uses, like libgtkmm, libsigc++, libglibmm and so on. Your distribution probably have a package for this and when you install it all dependencies should be taken care of automatically.
liblash LASH is a library and a daemon that synchronises file saving and loading in all your audio programs (or at least all programs that support LASH). It can be used to load and save entire audio sessions with several programs working together. Your distribution should have a package for this.

If the daemon isn't running when Dino starts you will not be able to save your session (and Dino will warn you about that). You should either set the environment variable LASH_START_SERVER to 1, or start the lashd daemon manually before you start any other audio programs.
libxml++ This library is used for writing and reading the XML files that Dino uses to store songs. You probably don't have this installed already, but your distribution should have a package for this too.