Can some one explain to me in plain English how the elements are formed in nuclear synthesis.
Well, most of the universe (matter that we can detect, excluding mass contributed by dark matter) is Hydrogen, about 75%. The rest is Helium, about 25%. Then there are trace amounts of other elements...
Most of this Helium was created quite quickly after the Big Bang by fusing Hydrogen in the so called proton-proton chain. You get protons slamming together, making Deuterium and Tritium, than those fusing together...
Other elements form in the centers of stars where the high temperature allows fusion of heavier elements. Still, you won't see every element fused there. For one, anything heavier than Iron cannot be fused, because it takes energy to fuse those elements instead of releasing it.
Elements heavier than Iron are cooked in Supernovae, when stars die. In that moment, temperatures are very high and there is a large burst of energy...
There are no elements in the universe 'lurking about'. Anything heavier than a certain isotope of Lead is radioactive - it will decay into lighter elements, so even if anything does form, it will eventually decay.
There's another reason there are no others lurking about - the higher the number of protons and neutrons in a nucleus, the more unstable the nucleus tends to be. We've had some success making very heavy nuclei in a lab - up to element 118 - but we're having trouble getting higher, because the elements we use to build heavy nuclei already decay before we can get them any higher...
Hope this answers your questions...