You can learn the Zone System tones and typical subject matter, and when the scene is nearby you can explore by walking close to things and taking close-up reflected readings, and "place" the readings on their usual Zones.
Originally Posted by sygyzy
The first thing you can try is... meter the palm of your hand in the light with reflected light. "Place" it on Zone VI. (Open up one stop to give more exposure than meter reads). Logically, you know your hand is bright and if you were to use a bright reading as-is, you would underexpose the shot. So you open one stop when you meter your hand. Now switch to incident mode and take your reading normally pointing at the camera.
If you did it right, the readings should agree - and this should boost your confidence.
I've recently been using a Master II meter with Zone Sticker, and have been enjoying this technique of reflected light reading - without necessarily requiring a spotmeter. The digital interface of your meter isn't as easily adapted to Zone System stickers.