Have a red handy. Red units can usually tank at least one hit from a green mage thanks to type advantage, as long as they don't get doubled. Reds that have Triangle Adept like Roy take very little damage from greens.
As for fighting them, you can either try to stay out of range and let them walk into your range themselves, or you can place a unit who can tank/counterattack them so that they get baited into walking forward to their deaths. I'm not that comfortable dealing with green mages either because my team is very blue heavy, so I try to stay out of range and wait for a chance to go in with my red unit.
Another option is to fight them with your own mage. Red mages are an obvious choice, but if you don't have a good red mage, green mages with Green Tomebreaker also work.
Mobility is a big thing, since they're ranged and you usually need to get your green counter in position really fast if the mage is in range. Bring a dancer, or consider putting movement support skills like Reposition/Shove/etc on some of your guys.