power chords, barre chords and according to my lead guitarist "chords that no one will use other than punk bands" which i have no clue what the technical name would be.
also chord progessions will help, no matter what era or type of music yur playing when it comes to rhythm guitar.
well, it really depends, because there is a wide range of rock and metal from 80's. if you wanna play van halen, you're gonna need some serious skills like speed, tapping, alternate picking, but if you just wanna jam to some motley crue you can learn some basic guitar skills like power chords and picking, chords, and you're good to go. you could probably just play the root notes to any van halen song and improvise, so you need good aural skills to recognize patterns in the lead guitar and back it up, and that is key for rhythm guitar
It's all about feel
The way i come up with a lick or progression is if either my co-guitarist or I come up with a nice chord. Then i play something over it in the same key. So, if you play a cool sounding chord or chord progression, tell him what key its in and it might be easier to come up with stuff (on his part).
I you want to play rythm, try to vary from the lead a little. or else they wont be able to hear your guitar at all untill the lead solos.
you'll notice a lot of metal rythm guitarists hold the same hand shape (for a power chord or barre chord) and smiply progress up and down the fretboard. if thats where your at in your development or you just like that sound and dont care about the simplicity, keep that same hand shape and focus on your stuming pattern(right hand).

try listening to some folk music (really) for the strum patterns. count out their patterns and play those patterns (to your song or the song you're copying). try and deliberatly cont out as you strum also: 1...2...1,2,3,4 1...2...1,2,3,4 et. cetera for whichever patern you come accross or happen to enjoy.