How do you roast coffee?

Outdoors!

To paraphrase Mark Twain's Connecticut Yankee in King Arthur's Court: there's more than one way to skin this cat. A few ways of roasting that come to mind are to roast the green beans...

• over a fire in an iron skillet (remember Dances With Wolves?)
  
• in a hand cranked popcorn popper on your stove
• in a hot air pop corn popper
• in a purpose-built hot air roaster (called a fluid bed roaster)
• in a purpose-built and sophisticated gas fired drum roaster
• or a simpler version like a BBQ mounted drum on a spit
  
• in a purpose-built electrically-heated drum roaster, either inductive or radiated
• in a flour sifter with a heat gun (yes, I'm serious!)
  
• and, according to Thompson Owen of Sweet Maria's, you can even use a gas fired oven
• or a last resort, with a heat gun and a dog bowl!
  

Flour sifter roaster

What won't work is a microwave or anything that involves water directly. And roasting in your oven will get it done but (as linked above) the likelihood of a good tasting roast is doubtful. But I've never tried it, so you might give it a whirl (good luck getting rid of the smoke!).

In each of these cases heat is applied to the outside of the bean to raise its internal temperature fast enough and hot enough that it doesn't bake. Baked coffee beans are not good; to guard against that you have to keep the heat constantly rising till the beans are ejected at the end of the roast. When the beans are ejected/dropped/dumped at the end, you have to drop the bean temperature rapidly or they'll continue roasting while they sit in the cooling tray.

At the most basic level, roasting is managed via sound, smell, color and (at the high tech end of things) temperature. Many (most?) home roasting appliances have at least a little viewing window to watch the progress of color change. And there's enough air escaping from these roasters that you can smell the changes in roast level. Hearing roast progress can often be a problem because of incidental noise from bean movement (reducing bean movement invites scorching which will kill a roast). And yes, there are more than a few of us that need hearing aids, but that makes it easier not harder.

Most anyone willing to try can do all these things. Those that are skilled at it, however, have moved the basics up at least one level. Those basics are something like this:

• For sound, detecting first crack (1C) isn't all that hard once you've done a roast. 1C has a distinctive cracking/breaking sound that occurs when the wall of the bean expands, opens the seam of the bean (properly a coffee bean is a 'seed'), and portions of the bean physically crack. Second crack (2C) is harder to hear. It's not as loud and is more of a snap than a crack- like a tooth pick being bent till it snaps.
• Smelling the progress of the roast takes some experience, but the basics are the grassy smell that comes with losing water during the 'drying phase'. That fades as the beans get hotter and approach 1C. Now you start getting the early smells that are characteristic of the beans from a certain region or plant variety. As the roast progresses toward the end (the roast can end anytime after 1C), more and more volatiles come off the coffee and identify the roast progress.
• Color starts out green (hence 'green beans') then moves first through a yellowing phase, then into tan. This is where the beans are drying and starting to roast. After that the tan morphs into progressively darker shades of brown as you approach 1C. As the roast continues, the beans become darker and darker brown, eventually passing through 2C and then to black. Continued long enough the beans will ignite in the roaster.
• Temperature requires some instrumentation. And that can be either very simple and can become more and more complex till it approaches the level of a science lab.

Since I lack the trained experience that leads to sophisticated roast management using smell & color, I have to rely on sound and temperature. And that points me toward a roasting machine that offers a temperature measurement and some way to watch the beans while they roast.

Thompson Owen of Sweet Maria's has done a great job detailing all these steps. There's years of reading available on their site but I found Using Sight to Determine Degree of Roast of particular interest, especially since the article includes corresponding temperatures that seem very close to the temperatures displayed using the infrared sensor as well as photos of samples pulled from the roaster during the roast.