Wishes (or regrets) about the past use Past Perfect:
I wish I had asked her out.
That's the easy part. For the other tenses, the general rule is to use Simple Past for wishes about the present:
I wish you were here.
and "would" for wishes about the future:
I wish you would come tomorrow.
However, the line between the two latter cases can be a bit blurry without an explicit time indicator, as most wishes for something in the future can also be applicable to the present without much of a change in meaning:
I wish it would stop raining (sometime soon) / I wish it stopped raining (now)
Additionally, when our "wish" is a request towards another person, using "would" makes it more polite:
I wish you stopped correcting me. (more firm) / I wish you would stop correcting me (more polite)