If you are a legal permanent resident of the United States who wishes to travel out of the country, such as to visit family who do not live within the U.S., you do not usually need to make any special arrangements with the immigration authorities. Freedom to travel is among the benefits of having a green card. But you must be careful about the length of your trip. If it lasts for a year or more, U.S. immigration law raises a presumption that you meant to abandon your U.S. residency, and you can be denied entry at the airport or other U.S. border.
Circumstances may arise that get in the way of your return within 365 days. In such a case, you'll have a chance to argue that you didn't really mean to stay away so long. Your best bet is to get in touch with the U.S. consulate in your home country before traveling back to the United States. See the State Deparment's instructions for returning resident visas.
But if you can tell in advance that you plan to spend more than 365 days outside of the United States (but less than two years), you should apply for a reentry permit. Make sure to do so prior to your departure, and to leave several weeks to allow USCIS to call you in for biometrics (fingerprinting). However, it's not necessary that the permit be mailed to you in the United States -- you can designate an overseas address, or choose to have the permit sent to a U.S. embassy or consulate in your home country.
The reentry permit will allow you to reenter the United States without facing questioning from the border officials regarding why you stayed away so long and whether you have abandoned your U.S. residency. It's good for a maximum of two years.
First, you must have a current immigration status that entitles you to a reentry permit -- namely that you are a U.S. lawful permanent resident or a conditional resident. If you hold any other type of immigration status, you will either not be eligible for or not need to apply for a reentry permit.
The application for a reentry permit is made on USCIS Form I-131, Application for Travel Document. Note that this form is used by various different types of applicants, so there will be parts of it that you don't need to fill in. The USCIS website will give you complete instructions on how to fill out the form, the current fee, and where to send it when completed. Also see Reentry Permit Process for U.S. Permanent Residents.
(If you're looking to travel and want some tips, see Leaving and Returning to the U.S. with a Green Card.)
If you have any unusual circumstances, it's always a good idea to speak with an immigration attorney to head off any potential problems upon returning to the United States.