As others have noted, the first thing you need to do is determine your focus. What type of criticism are you writing. For instance, if you are focusing on a specific writer, you might begin by deciding which writer you wish to focus on. The, you can proceed in several ways, but two easy options are to choose a theme that is prevalent in several works by that author or tie that author's place in history or his or her personal life to elements of the works in question. Essentially, what you are looking for is patterns. You will find that most writers develop themes that reappear in all or most of their works, which makes it easier to identify them if you have read several works by the author in question.
On the other hand, if you are focusing on a specific work, then the first thing you need to do once you have decided what work you will be writing about is to look for themes, images, motifs, something in the plot or characterization that interests you and that you can make some sort of claim about (this will be your thesis).
As to research, a look at what other literary critics have said about the author or the work is a good way to generate ideas as well as to find proof from other sources that helps to support your ideas. Just remember that anything that you gather from research must be appropriately cited!
Are you wanting to write criticism on the WRITER or the WRITING? This is important, because you might proceed in different ways.
If you are writing a criticism on a specific WRITING, then this means you would be critiquing an individual work by a particular writer. In this case, you would need to find out information about the writer - the writer's style, the genre in which the writer writes, the themes the author is concerned with, and finally, how representative the particular work you are critiquing fits into the body of the writer's work. You would also critique the work for its literary merits. Is it well written? Are the themes profound? Is the plot engaging? Are the characters well-defined and complex? Things like that. You would also find out what other critics say about the work. This involves research. Sometimes there is scholarship available on the work, and sometimes there is not. If it is a fairly new work, you can usually find some criticism by lit critics such as The New YorkTimes Book Review or The Washington Post, The Tribune, etc.
If you are doing a criticism of a writer, then you should read multiple works by that writer. Some of the elements listed above are germane, but in a broader sense. What are the writer's themes that appear in his/her works? How well have the writer's works been accepted by critics and scholars? Is the writer's stature one that will endure in American, British or World literature or is the writer a popular writer whose works may not endure? Things like that.