Calm down.
So the situation is this. You have a graphics card - one that is rather old (because they were stopped being produced a few years ago, as well as what looks like corrosion on solder joints in the photo you provided - signs of many many heat/cooling cycles ie: its been used a lot, because graphics cards regularly go above 70C in use).
You have seen pads where you believe a part has chipped off, but as many cards have unpopulated parts, some here have concluded that it wasn't there in the first pace based off other pictures of similar cards, and you wish to know what cap it was and what to replace it with. Others have stated even if it was chipped off it is very unlikely that this is the cause of the cards failure.
I'm inclined to agree with the above. Graphics cards are extremely complicated (that isn't patronizing, very few engineers will ever design anything even remotely close) and tend to be run at their limits - often getting very hot with hundreds/thousands of heating cycles over their life time. The PCB can warp, solder joints can crack, thermal paste can dry out leading to hotspots and over heating etc.. there are plenty of failure modes, and one small decoupling capacitor is extremely unlikely to affect its operation to the point where it will fail.
However... if you are convinced the missing cap is the problem, then by all means, replace it, and if it "fixes" the problem, then we can all eat humble pie
Firstly measure its size, as you want a cap that can actually fit on the pads. Looks like an 0805 to me but its hard to tell because gfx cards these days are so massive. You could probably get them in small quantities, so maybe 1uF @ 25V.
Next is the hard part, soldering it on. Unlike many two-layer boards, graphics cards (as well as motherboards, and almost all complex computer hardware) have multiple layers - many layers of copper traces, power planes, signals etc.. that gives them wonderful thermal conductivity - this is also used to spread the heat generated from the GPU and the on-board power supply to the whole board. The upshot of this is that when you try to solder to it, it will spread the heat from your iron outwards making it extremely difficult to bring the pads up to temperature. You will need a high wattage iron, or a hot air station with a narrow nozzle (and you will need to mask off the rest of the board).
You *might* be able to "fudge it" with a cheap soldering iron and get just enough solder to melt to hold the new part on the board, at least enough for you to test the idea that this missing cap is the cause of its failure.
tl:dr; You'll need some 0805 caps. A relatively good (as in 50w+) iron or hot air, and some thin solder to put the replacement part on. And then it is very doubtful this will make a difference to the cards condition.