Q: Is there an installer for SQLiteStudio?
A: No, there is no such thing. It's not required, since all you need to run SQLiteStudio is download it as binary distribution from download page and just run (unix users needs to set execute flag for the file before execution).
Q: How to run SQLiteStudio from sources? Should I compile it or what?
A: No. Tcl is Scripting Language, so no compilation is needed. What you need is Tcl installed in your system and couple of Tcl extensions.
All extensions (and Tcl core) is included in ActiveState's Batteries-Inluded Tcl distribution: ActiveTcl ( http://www.activestate.com/Products/activetcl/ )