In the early days of America, divorce was relatively unacceptable socially. The law evolved a means to obtain a divorce almost as a remedy for damages, if a spouse could prove infidelity, abandonment, neglect, abuse or some other such cause. Today, many states have no-fault divorce where the wide leeway of "irreconcilable differences" is grounds enough for divorce, and consent of the spouse is not necessary. In fact, most disputes in these cases are actually about the division of property, not the divorce itself.
File for divorce. Regardless of the state in which you were married, a divorce petition should be filed in the local state courthouse of the state of your current residence.
Serve the papers to your spouse. A divorce cannot proceed unless the spouse has been notified of the filing by proper service of the petition. Consent is not necessary, but the spouse has a limited amount of time to respond after service. If a spouse cannot be located after legitimate effort, the court will probably require notice of the divorce published in local periodicals before the process can go forward.
Bar objections. If the spouse fails to respond after service of the petition, you can seek an order from the judge barring him from objecting to the divorce. If this happens, the divorce will most likely be granted, even if the spouse eventually objects further down the line.
Claim irreconcilable differences. Usually, a court will grant a divorce on the claim of irreconcilable differences ("irretrievably broken" in some jurisdictions) even if only one spouse makes the claim. The court will not even necessarily investigate what those differences are, but if your spouse objects to the marriage, that in itself can become the basis for a claim of irreconcilable differences.
Modern legal culture regards marriage as a mutual relationship freely entered into, and therefore most states will not place a high barrier or burden of proof on a spouse seeking a divorce, even in states that are not strictly no-fault divorce states.
If your state does not offer no-fault divorce, it's a good idea to consult a legal professional prior to filing the petition to protect your rights in the process.