OpenGL Rendering Basics

You should be using RGBA mode, not color index mode, so pass GLUT_RGBA to glutInitDisplayMode

To enable Z buffering:

        glEnable(GL_DEPTH_TEST);
        glDepthFunc(GL_LESS);

To clear the screen:

        glClearColor(0, 0, 0, 0);
        glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

All OpenGL commands that actually do drawing go between glBegin and glEnd. All commands that set up state go outside glBegin and glEnd.
Many OpenGL commands can take inputs of various data types - the type is determined by the ending of the command: glVertex3i vs. glVertex3f vs. glVertex3fv