A little photo guide about how I do it :-) Dedicated to Datsun 1600 - thank you, dear friend

You will need a classic transformer soldering iron, no less that 75W. I use this oldie one for 26 years:

The prolonging of the soldering iron tip is necessary - additional resistance stop overheating the soldering tip too much.

Some resin is need too:

And a little bit of tin:

And tin suction tool:

...and of course replacement caps and something with bad caps. In this case I choose very simple recap of Jaton GF2MX400 card. Of course this card is phased out and you will probably not made and 3DMark world record with it, recapped or not, but for testing or normal office use it is perfect. Thanks to it's passive heatsink and small size it is preferred graphic card, where you need just one to be. I use these cards in folding and testing machines ;-)
I do, on the top of that, use a little osciloscope 440 Scope Plus http://www.atcweb.com/tpi440.htm - http://postimg.org/image/qc1qqciol/ ;-)

So, let's first take a look at the card itself:

As you can see, we gonna need:
1x 1000uF 6.3V d8 Samxon GC
4x 470uF 6.3V d6.3 Samxon GD
3x 10uF 25V d4 Samxon ZS

Let's take a look at the original caps...

...well, it is obvious they gotta go. Asiacon is the same as Evercon and this is the same cr*p as G-Luxon... :-(((

Step first - desolder with the soldering iron the caps:

Every time before use the soldering iron, dip it to the resin to protect against oxidation not only the contacts, but the actual soldering iron how wire tip. Result did not look ver pretty, but caps are gone now :-D The white or shaded (or other way highlighted) holes are typically for the negative cap polarity wires. Of course you gotta stay alert for exceptions and crazy designs, witch can swap the polarity! Sometimes it is better first take a picture of the card to have proof on how it looked before... ;-)

Now come the hardest step - suck off tin from at least one of the holes. Choose the one that is isolated from the rest of the PCB. This way you heat up most only small piece of tin and PCB and hence you should be able to suck the tin off easily.

Result - one hole is free.

Now take the replacement cap - take care about the polarization (on some cards, such as Gigabyte FX5200/FX5600XT, it is contrariwise!). Caps has one longer leg, that is the positive wire. If you have free the positive hole, you are good to go. Insert the longer positive wire inside and the negative adjust to be pressing exactly against the tin in the not free yet hole. Apply only light pressure. If you need more pressure, shorten the wires, but leave the positive wire longer.

From the bottom side heat up the tin in the negative hole and after a while (depends how big area of PCB you heating up) the cap nicely slide in place. Looks this way:

If you got free the negative hole instead, then cut the positive wire of the cap in middle, so it get shorter that the negative wire and then work it out same way.
Caps wires should be put thru to the end. Exception from this is only when you solder smaller or bigger spaced cap into holes that did not match. In that case - depends on how much the wires are getting dilate or closer - leave at least 3mm for the bend. Pressing too much in this case is very likely to damage almost any cap!

When you have the cap in place as it should be, then cut off the remaining wires. Leave just about 1mm from them. And then with plenty of resin again solder them.

Now it does not look pretty at all, right? :-( Well, let's continue till we have every caps soldered first.

Now will come the technical spirit in action. Using brush add the spirit in place where the resin is:

And leave couple of seconds to take effect. You can see that the resin is breaking up and melting already. You can help big chunks get off by sharpened piece of hard wood - notably increasing the rate how the resin leave the PCB.