The SWT Linux port is based on the GTK.
The natives are build using make and (by default) gcc.
SWT is made up of 2 parts, Java and the natives (written in C).
Java Part If you only make changes in the Java part or need to configure SWT for running snippets, then you don't need to recompile the natives, instead, you can just use the pre-compiled libraries in the binary repository.
Natives Part Make sure the binary project for your platform is imported and open in your workspace.
You need to install the following on your system:
Import and build the SWT project bundles/org.eclipse.swt in Eclipse. See the platform independent Readme for how to set the .classpath. This will populate the bundles/org.eclipse.swt/bin/library with the native code and build files.
To build SWT natives run the build.sh script in ./bin/library directory. To use the locally build natives run the build script with the ‘install’ argument (./build.sh install) or --help to see more options.
You can find additional information on GTK SWT development can be found in Eclipse Wiki.