Best way would be using FBOs, for better performance and some coding style issues whatsoever.
If you are not interested take a look at this code. It is from the days when I was much younger!(and didn't know FBOs exist)
int shadowMapWidth = 512;
int shadowMapHeight = 512;
glGenTextures(1, &m_depthTexture);
glBindTexture(GL_TEXTURE_2D, m_depthTexture);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_NEAREST);
glTexParameterf(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP);
glTexParameterf(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP);
glTexImage2D( GL_TEXTURE_2D, 0, GL_DEPTH_COMPONENT, shadowMapWidth, shadowMapHeight, 0, GL_DEPTH_COMPONENT, GL_UNSIGNED_BYTE, 0);
glCopyTexSubImage2D(GL_TEXTURE_2D, 0, 0, 0, 0, 0, 512,512);