We can use 'wish' with the infinitive to mean 'would like' or 'want to'. This is very formal. We don't usually use a continuous tense with 'wish' in this case.
I wish to speak to the school principal. (This means the same as 'I would like to speak to him/her.)
I wish to go now. (This means 'I want to go now'.)
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 was (were) rich.
She wishes her son was (were) smarter.
Watch the movie segment and write down a few sentences about what the characters wish to do.
MOVIE SEGMENT DOWNLOAD - INTO THE WOODS