Note: none of these methods are foolproof. Try a little of anything you eat before eating a lot of it.
Plants
Avoid leaves and stems.
It seems that these are not only typically inedible in general, but there is a laundry list of plants whose have roots or fruits that are edible, but with toxic stems and leaves. This is because generally they want to attract animals to eat the 'berries,' but not themselves. Also, plants may tend to want their seeds spread, but not their 'bodies' eaten, so the toxins would be in the leaves and stems. Of course, this is a huge generalization.
Watch what the native animals eat.
This is not fool-proof. But if you watch the berries, fruits, and vegetables (and others?) that a variety of animals can consume, these would be likely to be more viable to your palette.
Roots and Legumes
These have less likeliness (although not always) to be spotted by birds and large mammals, and therefore have not needed to develop a poisonous defense against them. Obviously some animals do root, so be careful, but there is less defensive interaction between them and animals in general.
On your island or whatever, the tropical plants might be good anti-biotics, because they don't have a frost to kill off some bacteria seasonally. This holds a good medicinal purpose.
Plants with other defenses
If you think of a bright berry, versus a highly placed, well-shelled fruit (say a coconut), the defense of the berry might need to be poisonous as they're largely vulnerable. Again, I say this is just as advice, as obviously you can eat a strawberry.
Animals
"Swarms and Herds"
Think of a school of fast, small fish versus a wandering stonefish. The former survives natural selection by having a large number of offspring to ensure that some will survive, while the latter survives largely by being toxic.
Watch what the other animals eat
(see above in plants)
Select the right parts to eat
On Earth, muscle and fat (although not always) isn't carrying as much blood and waste as it is nutrition. Avoid, in general, the organs, and go for the muscle and fat.
Other
Variety
In order to ensure you get the right nutrition, try a wide variety of foods.
Insidious
Select the weakest link and have them do the taste-testing. Keep cycling through testers until you've found something you can eat. You'd probably only lose one or two unlucky ones.