If the commute is short and the commuter is in a city or there are bike stores near the route or public transportation, all they really need is a bike.

I have a 4 mile commute each way, when I started out I had the bike and a backpack and that was it. There are 2 bike stores along my route (plus two more next to my condo). So if I get a flat there is a bike store within walking distance. But I do have tools , a spare tube, and a few CO2 cartridges in an under-the-seat bag. That's about the only necessary thing if you can't rely on a nearby bike store or bus.

But once I started riding a while I upgraded things. Got fenders, lights, a rack and panniers, performance clothing. All things to make it easier on me. But when I started, I had no idea what would happen, so I got my old bike out of storage (no tuneup or checkup) and threw stuff in a backpack and started riding.

As colleen c points out the biggest thing is to get started and have a good attitude.