You need to start by installing the packages you need for software development in C.
I don't know Zenwalk at all. In a typical distribution, you might need a package for the gcc compiler itself and another package for header files and/or binary.
Start with the package management portion of the Zenwalk documentation:
You may want to program in C using a text editor to edit the source code plus command line for compiling. In that case you'll need to select a text editor you are comfortable with.
Alternately, you might prefer using an IDE, such as CodeBlocks. That combines a text editor and build tools and debugger and other tools for software development into a uniform GUI environment. An IDE is likely harder to get installed correctly than just a compiler plus editor and harder to learn the very first basics of use. But an IDE makes debugging easier and makes it easier to move from the very simplest programming toward an intermediate level.
There are lots of online tutorials for C programming. You should find one that fits your approach. There are a bunch that are too closely tied to DOS or too closely tied to Windows and/or Visual Studio. Avoid those. If you want to use an IDE such as CodeBlocks, find a tutorial that uses the same IDE. If you don't want to use an IDE, find a tutorial that doesn't use an IDE.