Start with plausibility. Ask whether the colour you're looking at occurs naturally in that mineral at that intensity. Vivid blue quartz, jet-black "obsidian" points that are too glassy, neon-bright agate slices; these are colours nature rarely or never produces in that species, and a colour that shouldn't exist is your first flag. Knowing what a mineral's natural colour range actually is does more than any test.
Then check the price against the claim. Fine natural colour is rare and priced accordingly. A deep, even, "perfect" colour at a low price is usually telling you it was helped; genuinely top natural material doesn't sell cheap. Price that seems too good for the colour on offer is information.
Then look closely at the surface and the breaks. Dye collects in cracks and concentrates along fractures; run your eye over any chips or natural openings and look for colour that's pooled rather than grown. Coatings sit on top of the stone and scratch or wear at the edges, and produce metallic sheens no mineral makes.
What none of this catches is heating and irradiation. Both change the material from within and leave no surface trace; there is no fingertip test, and anyone who tells you they can always spot heated citrine by eye is overselling. For these, you are relying entirely on the seller knowing the treatment and stating it. That isn't a gap in your skill; it's the limit of what any eye can do, and the precise reason disclosure isn't optional.