Listen to your favorite '80s tunes. The best way to write in a certain style is to immerse yourself in it. Research the top hits of the decade and write down similarities you hear.
Decide the genre in which you want to write. This decision will tell you what kind of instrumentation you need to have. If you are going for a new wave or synth-pop sound, you will need a synthesizer. Get some guitars and a drum set if you want to do some '80s-style rock and roll. Buy a distortion pedal if you want to try thrash metal.
Write a riff or catchy tune. Most hits of the '80s feature a singable and memorable melody. Keep the melody simple -- complex or lengthy melodies are less likely to be remembered.
Write a chorus that goes along with your tune. The chorus might be the same as your melody.
Write the lyrics for the rest of your song based on your chorus.
Turn on a drum machine and sing your lyrics over the beat. Play a simple chord progression on a keyboard or guitar while you sing. Add your riff or tune to the mix.