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The best way is to keep them in an airtight glass jar with brine or olive oil. If you've already opened them, make sure they're completely submerged in the liquid, because olives that are exposed to air oxidize and look bad pretty quickly. The oil or brine acts as a protective barrier.
Put the jar in the fridge and they'll last quite a while that way, usually between two and three weeks without any problems. If you see mold starting to form or it smells off, better throw it out. It also works if you change the liquid every so often, especially if you notice it looks cloudy or has weird particles floating around. Either way, try to use a clean jar from the start to avoid contamination.
Another option if you don't have brine on hand is to cover them well with olive oil alone, though this method doesn't last as long as with brine. The important thing is that the container is airtight and everything stays under the liquid, nothing exposed to air.
Do you have a jar with a screw-on or airtight lid at home? What works really well is that once you open the container, you keep the olives submerged in that liquid (brine or oil) and seal the lid tightly every time you grab some. I've had an open can in the fridge for weeks now and as long as they stay submerged without touching the air, they keep fine. If you see mold starting to form or it smells off, toss whatever's floating on top, but the ones under the liquid usually stay good.
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