How to detect Zika in mosquitos
The gold standard would be the isolation of infectious virus from mosquito saliva. Extraction of saliva from mosquitoes is fiddly if you have to do it in containment and the survival of mosquitoes collected from the field may be low. Alternatives, in roughly declining order of strength-of-evidence, would be


identification of virus from dissected salivary glands,
identification of RNA from saliva/salivary glands,
identification of virus or RNA from heads,
virus or RNA from whole bodies of insects that are not visibly
engorged with blood (and we're getting
into not-very-reliable-at-all territory at this point).
detection of viral RNA from pooled field-collected (unsorted) insects, possibly including those which have recently blood-fed.


There are also other technologies that are beginning to be used for field surveillance of arboviruses in vector populations, such as sugar-coated or honey-coated Whatman FTA cards (mosquitoes sugar-feed on the cards which preserve RNA).

Two other things are worth emphasising here. One is that not all mosquitoes which ingest infectious virus will develop a transmissible infection even if they survive to complete the necessary incubation period. Some will clear infection completely, others may develop a disseminated but non-transmissible infection due to the existence of barriers to replication within the vector's tissues (see this paper for a nice review).
The second is that the importance of a vector is not determined solely by its competence (the probability that a mosquito ingesting an infectious dose and surviving the extrinsic incubation period develops a transmissible infection) but also things like vector:host ratio, biting preferences, and typical lifespan. Vectorial capacity is more important (this is a recent paper pointing out the differences).