What's actually happening
The moon's phase is the changing fraction of its lit surface visible from Earth, on a cycle of about 29.5 days. Lunar calendars and moon-related folklore appear widely across cultures, but they don't share a single meaning: a full moon has been read as auspicious in some contexts and dangerous in others.
The modern Wiccan pattern
The common contemporary framing runs: new moon for beginnings and setting intentions, waxing for building and drawing towards you, full for culmination and clarity, waning for releasing and clearing, dark moon for rest and reflection. Meetings held at the full moon are often called esbats, in contrast with the seasonal sabbats. This is a widely shared modern convention. It is not an objective property of the moon, and you'll find practitioners who invert parts of it.
Different ways people work
Some practitioners mark every phase; some only the full and new; some ignore phases entirely and simply go outside and look. Others track their own patterns against the cycle and use whatever correlation they find, which is a more honest version of the same instinct. All of these are recognisable lunar practice.
Building a personal moon practice
A Pretty Little Wiccan approach: for three full cycles, do one small thing at the same phase each month and write two lines about how the month went. After three cycles, read it back. You'll have something better than a borrowed correspondence list — evidence about your own rhythm, which is the only lunar authority worth much for a solitary practitioner.
Practical notes
Cloud, cities and a busy week are not obstacles: the phase is happening regardless, and 'I couldn't see it' is a perfectly good journal entry. If a full moon lands on a Tuesday you can't use, work the evening either side. Nothing in Wicca requires precision here.