There are a number of ways to safely make your frets look shiny and new:
1. Start by masking off the fingerboard with masking tape. place the tape as close the fret as possible without going onto the fret.
2. The quickest and easiest thing to use is 0000 ("four ought") steel wool, which you can buy at Home Depot in an eight-pack or ten-pack for about $1.99. Three or four quick swipes will do the trick and not harm the fret at all. It will get you about 75% as bright as the next option--about how frets look on a bass in the store.
3. Alternatively, you can use a polishing agent like this:
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NOTE: Taping is important because this kind of polish wipes on white or pink, but wipes off jet black. You don't want that on your fingerboard.
4. When removing tape, be sure to lift the tape off going from the edge toward the center on both sides--don't rip it off like a band-aid, especially on vintage guitars, or you risk pulling off a chuck of laquer.
This is a quick and easy operation. And if your board is rosewood, this is also a great time to apply a bit of lemon or pure mineral oil to the wood to treat and protect it. Do this semi annually or annually, depending on your climate.
Enjoy!