Wish - present

You can use wish + past simple to show that you are not satisfied with a situation in the present.
The past tense is used to show that what you wish is not real - it is the opposite of the real situation:

Real situation: I am poor.
Wish: I wish I was rich.

Real situation: I have to work tomorrow.
Wish: I wish I didn't have to work tomorrow.

When using the verb 'to be', in more formal register, 'were' is used instead of 'was' after the pronouns 'I', 'he', 'she' and 'it'.

Reality: I am poor.
Wish: I wish I were rich.

Reality: It's cold
Wish: I wish it weren't cold.

However, in everyday spoken English, this is less common nowadays, and many people say,
I wish I was rich.
I wish it wasn't cold.

You can use wish + past continuous to show you are dissatisfied with something that is happening now or with a future arrangement.

Reality: It is raining. (Present continuous tense for something happening now.)
Wish: I wish it wasn't raining.

Reality: I'm working tonight. (Present continuous tense for a future arrangement.)
Wish: I wish I wasn't working tonight.

You can use wish + would to express you are not satisfied with a present situation and to emphasize you want it to change now or in the near future.

Reality: This person is annoying me. (Present continuous tense for something happening now.)
Wish: I wish he would go away.

Reality: It is raining. (Present continuous tense for something happening now.)
Wish: I wish it would stop.

Reality: The computer that I use at work is very old.
Wish: I wish they would get a new one.

Reality: My colleague is talking loudly on the phone.
Wish: I wish she'd shut up!

You can use wish + could + infinitive to express that you are not satisfied because you are unable to do something.

Reality: I can't dance as well as Joanne.
Wish: I wish I could dance like Joanne.

Reality: You can't take a holiday because you are busy at work.
Wish: I wish I could take a holiday.