This question is a little difficult to answer, as you can write an analysis about many different aspects of a work of literature. However, what I can do is give you some advice on how to approach analytical writing, and then give you some ideas about prominent themes in J.R.R. Tolkien's The Hobbit to analyze.
Writing an analysis paper is like forming an argument. There are a couple of general steps you should follow when you're working on this kind of assignment. First, read the work of literature you have to analyze. Then, think about your particular opinion of the book. Usually, this opinion shouldn't be general (don't just say it's a "good" or "bad" book), but should deal with an important theme, idea, scene, or stylistic aspect in the book. Then, you'll come up with a thesis. This might sound complicated, but a thesis is just your particular opinion about a specific point in a work of literature. In other words, your thesis is your main argument/what you think about the point you're analyzing. Once you come up with a thesis, you'll need to back it up by picking examples from the book that support your ideas, and then explaining what these examples mean and how they prove your thesis.
Here's an example: you could analyze The Hobbit by reading it as an example of the Hero's Journey (a specific sequence of events, themes, and motifs that occurs again and again in literature and is absolutely present in The Hobbit). A sample thesis statement, depending on what you actually think about the topic, could read as follows: "I believe that The Hobbit is an example of the Hero's Journey because it includes perfect examples of each stage of this cycle, including the Departure, the Initiation, and the Return." Then, the rest of your essay would involve presenting examples from the book that support this idea. For example, you could argue that Bilbo's unexpected party is the Hero's Journey's Call to Adventure, or that his heroism in Mirkwood is part of the Initiation stage. All of these could be great examples, as long as you thoroughly and logically explain how they support your thesis.
Don't worry if you don't want to write about the Hero's Journey in The Hobbit; that was just an example. There are many other things you could write about, such as the parallels between Tolkien's novel and the poem Beowulf, the importance of Bilbo's merciful refusal to kill Gollum, and more. If you're still having trouble writing your analysis paper, I'd recommend looking at eNotes' essay resources. They're excellent and could give you some more specific support.