The transitive form of the verb “shine” is ”shined.” If the context describes something shining on something else, use “shined”: “He shined his flashlight on the skunk eating from the dog dish.” You can remember this because another sense of the word meaning “polished” obviously requires “shined”: “I shined your shoes for you.”
When the shining is less active, many people would use “shone”: “The sun shone on the tomato plants all afternoon.” But some authorities prefer “shined” even in this sort of context: “The sun shined on the tomato plants all afternoon.”
If the verb is intransitive (lacks an object) and the context merely speaks of the act of shining, the past tense is definitely “shone”: “The sun shone all afternoon” (note that nothing is said here about the sun shining on anything).