Mines will do damage to your ships as soon as they enter the sector. You need Mine Sweepers (from Mines tech) to sweep the mines to be protected from them. Sweepers are rated as to how many mines they can sweep, from 1 thru 5. You want to have the ability to sweep at least 100 mines in your attack fleets (different ships and comps will stack
), as there is a limit of 100 mines per sector.