I just went through this process and it wasn't fun. Actually it's not that difficult. You need to apply for the Vietnam tourist visa here, and upload your main passport page and a photo without a background. Then pay USD $25 and within three working days you'll be granted the visa.
Where I went wrong was filling out the form in a rush. The webpage is horribly simplistic and doesn't offer a smooth user experience. I entered my first name where it says Full Name, having been used to First Name and Last Name as separate inputs.
Once I paid and clicked submit, I waited three days only to find out I'd left out my last name under Full Name. Silly me. Then I clicked "Amend" to make some changes and other parts of the form were changed, like my arrival date. I didn't imagine I'd have to review all other parts of the form again, so I just clicked submit again.
Three days later I finally got the visa approved, but the arrival date was wrong, and I'd already bought my ticket and was in the airline check in line when the ground staff told me the date was wrong. To my horror, I'd figured I would have to call off the entire trip.
When you absolutely can't wait for a Vietnam tourist visa to process
But there was one last hope. A travel agency in Saigon called Cheap Vietnam Visa actually processes tourist visas ON THE SPOT. But it isn't actually that cheap. With an hour before the plane was to take off, I opened my laptop, which luckily still had some battery left, and applied for the RUSH visa. I paid USD $71 to get it processed immediately.
They sent me a document by email that allowed me to board the plane, and said they would send an employee to wait for me at the airport in Saigon, who would process my visa on the spot.
So the whole flight I was wondering if this was all a scam or if there would really be a hero at the visa counter holding a paper with my name on it, who would help process my visa on the ground. I put odds of success at 30 percent.
Sure enough when I arrived, there was a young Vietnamese guy in a T-shirt and glasses holding a paper with name on it, even spelled correctly. He took my picture and my passport and 20 minutes later handed it back with a 30-day Vietnam tourist visa in it. Miracles do happen.