Here's Harvard's take.
Here's University of North Carolina Writing Center
One way to strengthen your argument and show that you have a deep understanding of the issue you are discussing is to anticipate and address counterarguments or objections. By considering what someone who disagrees with your position might have to say about your argument, you show that you have thought things through, and you dispose of some of the reasons your audience might have for not accepting your argument. Recall our discussion of student seating in the Dean Dome. To make the most effective argument possible, you should consider not only what students would say about seating but also what alumni who have paid a lot to get good seats might say.
You can generate counterarguments by asking yourself how someone who disagrees with you might respond to each of the points you've made or your position as a whole. If you can't immediately imagine another position, here are some strategies to try:
Do some research. It may seem to you that no one could possibly disagree with the position you are arguing, but someone probably has. For example, some people argue that the American Civil War never ended. If you are making an argument concerning, for example, the outcomes of the Civil War, you might wish to see what some of these people have to say.
Talk with a friend or with your teacher. Another person may be able to imagine counterarguments that haven't occurred to you.
Consider your conclusion or claim and the premises of your argument and imagine someone who denies each of them. For example, if you argued "Cats make the best pets. This is because they are clean and independent," you might imagine someone saying "Cats do not make the best pets. They are dirty and needy."
Once you have thought up some counterarguments, consider how you will respond to them—will you concede that your opponent has a point but explain why your audience should nonetheless accept your argument? Will you reject the counterargument and explain why it is mistaken? Either way, you will want to leave your reader with a sense that your argument is stronger than opposing arguments.
When you are summarizing opposing arguments, be charitable. Present each argument fairly and objectively, rather than trying to make it look foolish. You want to show that you have seriously considered the many sides of the issue and that you are not simply attacking or caricaturing your opponents.
It is usually better to consider one or two serious counterarguments in some depth, rather than to give a long but superficial list of many different counterarguments and replies.
Be sure that your reply is consistent with your original argument. If considering a counterargument changes your position, you will need to go back and revise your original argument accordingly.
Here's University of California San Diego's CA
Overcoming possible objections to your argument can thus take several forms. You might try to win your parents over entirely to your view, or you might find some way of accommodating their argument while still getting to have your car at school. You might, for instance, compromise on some parts of their concerns by conceding that your parents’ worries are justified, or by agreeing to install an alarm system to prevent burglary. Counterarguing, then, may involve some of all of the following:
• Anticipating your readers’ concerns: to persuade readers that your argument is reasonable, you need to begin by anticipating how they might think differently from you. What questions or doubts might they have? What alternative interpretations or arguments might they be tempted to find convincing?
• Refuting those concerns: You might argue strongly against the premises or the reasoning of an argument in order to convince someone that your position is preferable.
• Accommodating those concerns: You might find a way to agree with part of someone’s opposing argument without weakening your own argument.
• Conceding a point in light of those concerns: You might concede that someone’s concerns are justified and yet go on to show why those concerns need not matter or need not damage your main argument.