Know the law. Understanding what a trial judge in your state has to consider in an alimony case will help you focus your case and identify key weaknesses in your ex's claim. You can usually find alimony statutes in your state's legal code under "Domestic Relations" or "Family Law." Most states make their statutory law available for free on the legislature's homepage. The statutory outline of factors the court must consider in ordering or denying alimony will tell you where you need to attack the most.
Know the evidence. A lawyer would never try your alimony case without thoroughly examining the other side's financial affidavits, tax returns, bank accounts and pay information. As your ex's financial need is key, a lawyer would also develop a thorough understanding of what her standard of living during the marriage actually was. In order for you to do this yourself, you need to learn how to to draft subpoenas, get them issued and get them served. You'll also need to learn how to use other discovery devices, such as interrogatories (written questions for the other side) and document production requests.
Develop a plan. After you've educated yourself on alimony law in your state and gotten your hands on as much information as possible, make an outline of what you intend to bring out in court. List the points you want to make when you testify and write out questions to ask the other side.
Go to court and bring everything together. Hit each of the factors that a judge in your state has to consider and show the court how those factors favor you, not her. Use your knowledge of her financial condition to show that she doesn't need as much alimony as she's claiming, and use your own financial information to show you don't have as much disposable income as her lawyer says.