Quick answer
ver = to see; the image reaches your eyes, no effort needed. Also the verb for films and TV.
mirar = to look at, to watch deliberately; you point your eyes on purpose.
mirar needs no preposition: mirar algo, never mirar a algo for things.
Side by side
Memory trick
Did you aim your eyes, or did the image just arrive? Aiming is mirar. Arriving is ver — and screens count as arriving.
Typical mistakes
Anoche miré una película en casa.
Anoche vi una película en casa.
For a full film or a TV programme Spanish uses ver. Mirar una película sounds like you stared at it without following the story.
Mira a la pizarra.
Mira la pizarra.
Mirar takes a direct object with no preposition. The a only appears with people: <i>mira a tu hermano</i>.
Check yourself
Fill in: "___ esta foto, ¿reconoces a alguien?"