Dash attack is my main approach if my opponent is level with me. If they're above, I perform a dashing usmash. If they're below me, I'll get level or under them asap.
If your foe is farther away, pressure them with the stun gun. B-down is a nice approach for a surprise sex kick and invincibility frames.
If your opponent is shield grabbing your dash attacks, switch things up to grabs. Grabs are wonderful combo builders for Zamus. You can chainthrow with fthrow, just never do it more than twice in a row. Dthrow leads to aerial combos.
Dash attack is a better approach because it sets up for all of your tilts and dsmash. Dsmash sets up for pretty much anything you want. Tilts set up for combos.
shield>attack - attack>grab - grab>shield <--the rock paper scissors of smash bros (sorta)
uair, bair, b-side are my main killing moves. There are other ones, but these are the most effective.