You have received some pretty good advice so far, but the answers are not quite on the money.
The most common, most practical and best way to get to Hoi An from Ho Chi Minh City is flying to Da Nang and taking a taxi from Da Nang to Hoi An. There are two domestic carriers that fly into Da Nang, which are Vietnam Airlines and Pacific Airlines. As George mentioned, Pacific Airlines is no frills-low cost. The price difference is about $10, so you should be more concerned about departure/arrival times rather than cost. The flight is a little more than an hour.
Once at Da Nang International, DO NOT TAKE THE AIRPORT TAXI COMPANY. Instead, take the Mai Linh taxi company (green on white color scheme). Mai Linh has standardized rates that are competitive across Vietnam, while Airport Taxi will screw you for being a traveler stuck at the airport thinking that you have no other choice for taxi service.
Hoi An is about 10 miles from Da Nang and the taxi will cost you about $10. If you want to do something really smart, get a taxi coupon book from the Mai Linh office in Ho Chi Minh City. You can pay all of your taxi fares in Vietnam at the end of the month or when you leave and receive a 10% discount. Also, you won’t have to worry about carrying around change for taxi fare because you will write out a coupon instead.
You can also take a tour bus, train, private car and other means to get to Hoi An. All of the mentioned options will make for much longer yet more scenic travel to Hoi An. A word of caution though, Central Vietnam is susceptible to floods and road washouts due to typhoons, storms and heavy rains common to the area. Many of the tour bus companies and private drivers will operate despite the flood danger, which will put your life in jeopardy just to see the countryside at ground level. In my opinion, the jungle between Ho Chi Minh City and Da Nang looks the same as the jungle just outside of Ho Chi Minh City. Save yourself the worry and take a plane.
Have fun on your trip!
P.S. Welcome back Ong Jon!!!