' I wish to' can mean the same as 'I want to' but it is much more formal.
· I wish to interview the CEO.
· I wish to make an appointment with the new director.
You can also use 'wish' with a noun to 'offer good wishes'.
· We wish you a merry Christmas.
· I wish you all the best in your new job.
Notice that when you want to offer good wishes using a verb, you must use 'hope ' and not 'wish'.
· We wish you the best of luck.
· We hope you have the best of luck.
· I wish you a safe and pleasant journey.
· I hope you have a safe and pleasant journey.
However, the main use of 'wish' is to say that we would like things to be different from what they are, that we have regrets about the present situation.
· I wish I were in Oxford.
· She wishes she had more money.
· We wish we had learned about life in highschool.
Notice that the verb tense which follows 'I wish' is 'more in the past'.
I'm too fat. I wish I was thin.
To talk about actions that take place in the present, but you want them to change in the future. This structure is used to talk about another person, and generally about things you don't like.
Instead of 'will, we use 'would'.
· You keep borrowing money from me. I wish you wouldn't keep borrowing money from me.
· You’re always calling me too late at night. I wish you wouldn't
phone me so late at night.
In more formal English, we use 'were' and not 'was' after 'wish'.
· I wish I were rich.
· I wish she were happy.
Were" is used after "wish" — in all persons — when you are referring to a present situation that is a fantasy, that is untrue, that describes the situation the way you want it to be, not the way that it really is.