The first step
As soon as you decide to travel internationally, you need to get a passport. In the US is usually takes about 6 weeks to get a new passport, or if you pay for expedited delivery you could get it a little sooner.
If you already have a passport, check the expiration date immediately, so you can renew it on time if you need to. Many countries now operate online systems for applications which are simple to use if all the requirements are met.
Check to see if you need to get a travel visa. Many times it's possible to get a visa on arrival to your destination, at the airport. But other times you need to apply and receive your travel visa before you leave.
Age is also important when applying for a visa. If you are over a certain age, you may need a medical release, X-rays, and travel insurance. These take time to acquire, so start early.