Start with a core idea. This is something that will allow you to build a foundation you can build the rest of your song around. For heavy metal writers, the lyrics of a song are often the first thing written. Compose your lyrics in a notebook, leaving a blank line above each lyric line for chords. Many heavy metal songs start with a basic chord sheet, in addition to a rough recording of the song idea. As for lyric content, allow your mind to roam. Heavy metal lyrics have come a long way from being strictly about music, women and going to parties. Bands such as Metallica often write lyrics on politics, crime and other topics.
Write the main sections of your song on paper. You don't need to know music notation to do this. Many heavy metal players don't understand, or care, about music theory or how to notate music. Their focus is to write a song and find a comfortable way to translate it to the rest of the band. Work out the main riff, which is a repeating musical figure that gives your song its identity, down on paper, then write down any guitar fills (groups of musical passages often played on guitar) and solos. You can notate the music using guitar tab or simply by using numbers to indicate where your guitar player or bass player should play the fill. Drum parts are typically made up by the drummer in a heavy metal band.
Record as much of your song as you can to take to the rest of the band. Record as many individual instrument parts as you can using the actual instrument. If you have access to a bass, record the bass parts along with the guitar parts. The final process of writing a heavy metal song is often sitting with the band and bringing all the parts into a cohesive song. The more you have to work with going in, the easier it will be to polish the finished song.