First off, see the first paragraph of Inside Kuantan: Safety for some important information regarding visits to Malaysia. If you still want to go, read on.
American citizens traveling to Kuantan are required to present a visa validate for six months prior to arrival in Malaysia, unless your visit is for less than 90 days. At some point, you will be required to fill out a Malaysian Disembarkation Card to present before being allowed in the country. At this time, you will be given a "social visit' pass and you're home (or rather, Malaysia)-free. Depending on in-country travel (Sarawak, for example), you may have obtain a separate social visit pass. For more information on this pass, visit Ministry of Foreign Affairs Malaysia. Be sure to carry your passport, visa, and identification at all times, especially during an extended stay.
Kuantan's airport goes by the whimsical name, Great Circle Airport or (boringly) KUA. It is not an international airport, however, so, if you're flying into Malaysia, you will arrive in Kuala Lampur and take a shuttle flight to KUA . Malaysian Airlines runs flights to Kuantan several times a day, so there should not be much lay-over time. When you're reluctantly ready to leave Kuantan, give yourself plenty of time to return to the airport for departure.
You may prefer to take a bus into Kuantan, though the five-hour trip from Kuala Lampur is not recommended. TransNasional Bus Service will bring you directly to Kuantan's downtown. A new highway, called the East Coast Highway, has made overland travel more comfortable and convenient, whether your bussing or driving a rental car into Kuantan. Travel to Kuantan by water is another choice, so consider booking a relaxing cruise.