OK, in-camera meter.
Here is a way you might be able to do Zone System thinking with an in-camera meter:
1. Looking at the whole scene pick any shutter speed that indicates f/5.6 is correct for average.
2. Walk up to the darkest part of the scene that has to have detail (not pitch dark but the darkest thing).
3. Move the f/stop until meter says it's right. (That's Zone V). Click f/stops towards f/16 two or three clicks to "place" that reading on Zone III or II
4. Note the f/stop
5. Walk up to the brightest part of the scene that has to have detail (not a chrome shine but something light)
6. Move the f/stop until meter says it's right (Zone V again). Click f/stops towards f/1.4 two or three clicks to "place" that reading on Zone VII or VIII
7. Note the f/stop
If you get to f/5.6 both times, then just use f/5.6... If you get different choices, take the shadow reading and keep in mind where your highlight fell...
As everyone suggests, develop normally unless you really have N-2 (Bright snow next to a Cave - compensating development) or N+2 (Foggy Day where everything looks gray - develop longer than usual).