LaTeX comes with most Linux distributions in the form of the teTeX distribution. Find all packages with 'teTeX' in the name and install them.
Most editors such as vim or emacs come with TeX editing modes. You can also get WYSIWIG-ish front-ends (technically WYSIWYM), of which perhaps the best known is LyX.
The best quick intro to LaTeX is Oetiker's 'The not so short intro to LaTeX'
LaTeX works like a compiler. You compile the LaTeX document (which can include other files), which generates a file called a .dvi (device independent). This can be post-processed to various formats (including PDF) with various post-processors.
To do PDF, use dvips and use the flag -PPDF (IIRC - I don't have a makefile to hand) to produce a PS with font rendering set up for conversion to pdf. PDF conversion can then be done with ps2pdf or distiller (if you have this).
The best format for including graphics in this environment is eps (Encapsulated Postscript) although not all software produces well-behaved postscript. Photographs in jpeg or other formats can be included using various mechanisms.
