Register an Appearance
One option after you receive dissolution papers is to file an appearance with the court. An appearance is the simplest document you can use to let the court know that you want to be involved in the proceedings. In fact, this is pretty much all it says. It gives the court your contact information so you'll receive notice of everything that happens in your case. You can register an appearance in some states by showing up at the hearing even if you haven't filed any documents and the court has already scheduled the case for default.
Your other choice is to file an answer to your spouse's petition. Some states have forms for this, but you can also draft one of your own. It's a matter of answering each of the paragraphs in your spouse's petition for dissolution. Petition paragraphs are typically numbered to make this easy. For example, you can write the word "admitted" as your paragraph 1 if your spouse states in her paragraph 1 that you were married on a certain date and the information is correct. You can write "denied" in your corresponding numbered paragraph if she states something you don't believe is true. For example, she might state in her paragraph 9 that she can't make ends meet without a substantial alimony order. You would deny this in your answer's paragraph 9 if you believe she actually has ample income.
Counterclaims or Cross-Petitions
The most complex response you can file is a counterclaim or cross-petition. This document is usually submitted as part of, or in addition to, an answer. It acts as your own petition for dissolution, even though you didn't file for divorce first. You can offer your own grounds and ask for your own relief. For example, you can state in your answer that your spouse does not require alimony, and in your cross-petition, you can ask the court to order alimony payable to you instead because she actually earns more than you do. Filing a cross-petition has the added advantage of ensuring that your divorce can't be dismissed if your spouse decides to pull the plug on the proceedings for some reason. One of you would then have to file for dissolution all over again unless you file a cross-petition or counterclaim. This document keeps your divorce alive and active in the eyes of the court unless you dismiss it.
In some states, a petition for dissolution is slightly different from filing for divorce. For example, in Ohio, a divorce is contested; your spouse would file a complaint to initiate the legal action. A dissolution is uncontested because you've already agreed to and signed a marital settlement agreement. You and your spouse would jointly sign a petition for dissolution. You don't have to file a response with the court if you live in a state that allows joint petitions and you sign one. The joint petition lets the court know you're involved and explains what terms you and your spouse are asking for to end your marriage.
Unless you've filed a joint petition with your spouse, you're not done after you've filed your response with the court. You must then serve a copy of the response on your spouse, just as she served her petition on you to begin the proceedings. The rules for this vary by state, so check with the court clerk when you file your appearance, answer or counterclaim. Typically, the county sheriff will deliver your paperwork for you, but some states allow you to send a copy by certified mail, hire a private process server or even hand-deliver the papers yourself.