I often encourage my students to begin an analytical essay with a personal experience. Doing this can make the essay more interesting than a plain analysis and deepen its significance as well. The anecdote might say something about your conflicts with your mother. If you are a boy, your relationship is probably very different from that of the daughter in the story, so you could make an observation about that. It is important to provide a strong transition between your personal anecdote and the statement you make about the story. Here is an example: “Because my mother did not attend college, she insists that I do so right after high school. She assumes that I want what she wants, but I do not. I would rather travel for a few years before I go to college, and sometimes I consider taking on an apprenticeship as an artist, and this makes my mother very angry. She thinks she knows what is best for me, but I do not want to do as she wishes just to please her. The mother and daughter in Tillie Olson’s “I Stand Here Ironing” face a similar dilemma in trying to understand their different desires” And from here you would move to your thesis, about which other respondents have offered good advice.

First of all, this is a very general question. What type of essay are you writing? I'll try to help you as best I can. I usually have my students introduce the piece they are writing about first, and then go into their Thesis sentence, which is probably the most important part of the paper. You might try something like:
"I Stand Here Ironing" by Tillie Olsen is a monologue in which the narrator reminisces about her nineteen-years-old daughter's childhood and the effect she had on the girl,as her mother,while she irons. As she irons, she draw parallels for herself and the reader between telling the story and ironing the wrinkles from a dress. This story is interesting for several reasons.... Insert your Thesis here. You will need at least three WHATEVER (reasons, ideas, anything you choose to support your thesis).
Each reason, etc. will be explained in its own paragraph. I hope this helps you. Good luck. Brenda

You don't say if you have a thesis statement or specific topic you need to write about. Always look at the literary elements, such as characters, setting, conflicts, or themes.

One of the main themes of the story is the search for one's identity. Your specific thesis statement could be: "In 'I Stand Here Ironing', the mother and daughter are searching for their identity." Use specific examples from the story, such as the daughter becomes "somebody" when she is on the stage acting. Another example is the mother is looking for her identity as a mother because she doesn't know how to help her daughter. They would go in your body paragraphs, paragraphs 2, 3, and 4.