Critically examine The Scarlet Letter in terms of the theme love triumphs over various obstacles.
This sounds like a prompt for a critical essay. I encourage you to accomplish this assignment by spending the most time pre-writing, or gathering evidence, forming a thesis, and planning and organizing your essay. The theme of love triumphing over other various obstacles gives you two great subjects under which to gather evidence.
First, come up with a list of examples (use quotes where you can) of love triumphing. Certainly Dimmesdale's confession on the scaffold in the final scene of the story could be evidence of this. But there are several other examples as well. Hester's ability to remain a citizen of the town, raise her daughter alone, and eventually earn the respect of others (as the "A" comes to stand for "able") are all examples of love triumphing.
Then, think of examples of the obstacles that are overcome. Each character has his or her own set, so you can choose now or later to edit down your list by following only one or two characters. I always suggest gathering as much as possible so you know what you have to work with. To help you get started you might include that Hester must overcome shame and public shunning in order to move on with her life at all. Dimmesdale must overcome his own personal guilt, as well as live with the secret he holds.
Once you have two long lists, you can look at each and see if any patterns or categories begin to emerge. Circle ideas that are similar. Cross out ideas that seem to fit with nothing. Once you've edited down your list of examples into a few coordinating categories, use these categories to compose a thesis statement.
Now you are ready to outline your essay. Write a topic sentence for three body paragraphs (or more) that support your thesis statement. Include examples (from your original list) that support each topic sentence. Once you've accomplished these steps, the bulk of your work is done.
Feel free to post further questions here for help as you go, and good luck!