During fusion (in the Sun or in attempts on Earth), how is the repulsive effect of the strong nuclear force overcome? (I assume from the name that fusion is just the combining of nuclei, but please do say if I have this completely wrong)
the nuclear force is strongly attractive as pointed out by Michael Walsby above but as the nucleons come closer together it then becomes powerfully repulsive because of the Pauli exclusion principle. this means for the pair of attracting nucleons there exists a potential well with a "bottom" in it, and the distance at which the well bottoms out furnishes an equlibrium separation distance for the bound nucleons. This in turn is responsible for the fundamental size of nuclei in general.
Nuclear fusion occurs at separation distances larger than those at which the repulsive component becomes dominant, so that part of the potential does not have to be overcome in order for fusion to occur.
The strong force is not repulsive, but the positive charges on the hydrogen nuclei are. The problem on Earth is to overcome the mutual repulsion of like charges so that the nuclei can fuse. At the centre of the sun, this is easy, because the pressure is tremendous and the hydrogen, helium and other nuclei are crowded together, so collisions can easily happen. For the collisions to be violent enough for the nuclei to get really close, despite the repulsion, great heat is required. The temperature at the sun's core is 14 million degrees Centigrade, so the hordes of nuclei are darting wildly about in a very crowded environment, and collisions frequently occur. When the positively charged nuclei come close enough, the strong force takes over. It is about a hundred times stronger than the electromagnetic force, but has a very short range and is only effective within the nucleus In the grip of the strong force, the two nuclei combine. The nuclear reactions within the sun are rather complicated, not just the simple combining of hydrogen nuclei, so I won't go into the full details here.