For all types of athlete, their ability is determined by both genetic and environmental factors (nature and nurture). The degree to which each contributes ultimately depends on the demands of the sport.
As an example let's compare basketball and golf.
Basketball is likely to have a strong genetic component because players tend to be exceptionally tall (average is over 2 metres and there are only a handful who have played NBA under 1.75m). Because height is strongly genetically (but not entirely) determined by the genes, they have a big influence on whether someone can poses the physical qualities to play in the NBA. However, a large part of their technical capabilities are due to their environment. If you give a basketball to someone who has played 2 games a week their entire lives and ask them to take 10 shots it is likely they would score more than someone who has never seen a basketball!
Comparing basketball to golf, there are all sorts of body types within the PGA tour, and they is no/few obvious genetic traits which golfers tend to have over other people. This would suggest that golfing ability is more affected by environment.
So an easy way to get a rudimentary test of genetic contributions to sporting ability would be to compare frequency distributions of focal traits in the athletes to distributions of regular people. Obviously the phenotypic trait you measure has both genetic and environmental contributions (e.g. childhood diet) which could affect them but it would be a good starting indicator which could give some candidate traits to test.
As a scientist I would also consider sequencing some athletes and some non athletes and seeing which genes the athletes have more often then the regular person's genome. However, such studies are likely to be complex - linking phenotypes (in polygenic traits) to the single allele variants relies on large sample sizes. Generally it will be more difficult if:
- There is large variance in the trait
- The gene has a small effect (see major and minor effect genes)
Both of these problems going to be positively correlated with the number of genes affecting a trait (how polygenic is it?) which for athletic ability is probably quite a substantial amount of genes.
EDIT: Here are some possible studies for your further exploration of the topic-
Candidate genes for Specific Genetic Markers of Endurance Performance and o2max
Rowers have an excess of the ACE I allele
Elite Italian footballers with "explosive" leg strength also reveal ACE and other genetic markers
A precautionary tale about Genetic tests for athletic ability