A lot of the art in books depict dragons in the sky or following trains. How common are dragons in Shadowrun? Would people freak out seeing a dragon flying between buildings in Seattle? I've seen official art with dragons in the sky of Neo-Tokyo and Berlin and I'm just curious to know if this is typical thing to describe to my players.
Not very common, according to the Shadowrun wiki (emphasis mine):
Dracoforms are the various forms of large saurian creatures of tremendous intellect and magical power. What little we know of these great mythical beasts comes from the great dragon Dunkelzahn, whose famous 12-hour interview on January 27th, 2012 answered most of the world’s questions about dragons, the Awakening and magic in general. Dunkelzahn, however, was an enigma among dragons. Whereas most dragons are solitary creatures, more apt to see people and companies as ways to increase their wealth and/or power, the Big D was always in the public spotlight and led metahumanity through the dark years when magic first returned.
Also in the Runners' Companion it says:
Dragons are an influential and undeniable—if rare—part of the fabric of life in the Sixth World
There are around 25 named dragons in Shadowrun, some of them dead. The important thing to remember about dragons is that many of them are corporate CEOs, for example
Lofwyr is the CEO of Saeder-Krupp.
Would people freak out if they saw a dragon flying around their city? Most likely yes. Dragons spend much of their time in human form and generally only appear in their normal guise when resting or dealing with issues. For general Shadowrun descriptions, I'd suggest pushing the cyberpunk angle hard and only bring in the supernatural creatures when it's needed.
The 25 named dragons are most "Great Dragons". Figure about 10-40 "normal" dragons for each great dragon gives 250-1000 regular dragon so 275 to 1025 dragons total. I'd say closer to 300 than 1,000 though, since even regular dragons are going to be dying in the Shadowrun world.