I think a gardener can begin to distinguish between insect damage, disease and environmental stress by asking questions, understanding plant families and knowing your garden's 'normal'.
You could begin by asking; is the problem occuring in only one plant species, in plant families or in all plants throughout your garden? If the problem is found in only one plant species, determine if what you are seeing is normal or abnormal.
* Is the damage found throughout your garden? Is it found in the surrounding weeds? This may be signs of abiotic damage, like extremes in temperature (frost/heat), winds, excessive rain, drought, over or under watering, pesticide drift, salt spray etc. Or is the problem specific to a plant family, which may indicate more of an biotic situation.
* When did the problem occur? Did it happen all at once, affecting many different plants in your garden? (then it is most likely a one time issue and probably abiotic in nature.) Is it progressive? Is it spreading to other plants in the same family? (then consider a disease or insect infestation.)
* Look for any changes in the plants appearance, like leaf wilt, spots, lack of vigor, decrease fruiting or blooming, wounds, galls, witches brooms, death of leaves/stems, etc.
* Look at the roots for any discoloration, excessive branching, injured root tips.
* Look for any signs of disease/pests; things like mold, powdery mildew, spores underneath the leaf, insect eggs/webbing, larvae, aphids etc. Are there fruiting bodies like mushrooms/puffballs? Do you see any harmful insects in the soil?
* Search for photos and descriptions on reputable websites to see if you can find similarities to your findings.
If all else fails, contact your local Cooperative Extension office for advice!