Misconception. What people often call a "mini-stroke" is a transient ischemic attack which is just that-transient, it doesn't leave disability or imaging evidence. A non-cortical stroke in the white matter can go un-noticed until they add-up and cause memory loss and cognitive dysfunction. A cortical stroke, unless it was very small or in the front of the brain will usually cause some sort of symptom.
By history. Mini strokes don't cause permanent damage, so they don't show up on mri. Diagnosis is by history- temporary loss of nervous system function, causing numbness or weakness, drooping of half of the face, trouble forming or finding words, trouble reading or understanding, etc. It can be hard to tell from migraine, as that can cause similar symptoms. Mini-strokes are warnings, so see a doctor!