Juice the limes and oranges, either by hand or using a strainer, into a medium-sized bowl. Add the diced onion, garlic, basil, and salt to taste.
Chop shrimp into bite-sized pieces, and transfer them to the citrus juice mix. Stir well to fully coat the shrimp, adding more juice if needed to fully submerge them. Then set in the fridge until the shrimp is opaque.
The ceviche may be done in as little 15 minutes, but it can take up to 45.