1) Disassemble the GPU:

Disconnect the power cables from the graphics card and unroll the screws that hold your board and sink together. While doing so, the position of each screw must be remembered so you don't end up placing them in the wrong position.

The fan cable is now to be disconnected with the GPU cover removed. The task of removing the heatsink is a great struggle as the thermal paste that was applied earlier has hardened. Once you're done with that, wipe the dirt off that had been accumulated on the heatsink.

2) Remove the old thermal paste:

Clean the old, hardened thermal paste properly before applying the newer one. Many prefer using 90% Isopropyl alcohol to remove the thermal paste as it is considered to be very effective in doing this job. 

Apply this alcohol or any other thermal removal fluid you have on a lint free cloth and wipe until the old thermal paste has been removed completely. Cleaning the thermal paste is perhaps a time consuming task. Don't exert too much force on the GPU chip while cleaning it as it can cause damage to it.

3) Apply new thermal paste:

Once you have cleaned it thoroughly and the alcohol has dried, apply a little amount of thermal paste. The thermal paste should be applied in the right amount(size of a rice grain) at the center of the chip, such that when the heatsink is pressed, the paste would spread equally over the GPU chip. 

You don't need to spread the paste, it will automatically spread once the heatsink is placed over it. Bubbles should not be formed as they'll affect its cooling performance. The less the bubbles, the better it would be. 

Applying a lot of thermal paste will cause it to come out from the sides creating a dirty look. It shouldn't be sparse too as it will not spread well over the surface reducing its effectiveness.

4) Reassemble:

The last step includes placing the heatsink back onto the GPU and connecting the fan cable. You should be a bit more careful while mounting screws as they must be placed on their respective areas.

Tighten the screws and install the GPU back onto the motherboard. Keep in mind that you don't over tighten them.