First, find the sign and degree of your Moon and Sun on your birth chart. Then plot these on a blank wheel, using the Sun and Moon glyphs. What you'll be discovering is where the Lights were in relation to each other at the time of your birth.
I'm using my own chart in this example above. This shows the Sun in Cancer at 12 degrees and the Moon in Gemini at 11 degrees. You can move counter-clockwise from the Sun to the Moon to figure out your Moon phase. Count the degrees from the Sun to the Moon, keeping in mind that each sign has 30 degrees. In this example, the Moon is 329 degrees ahead of the Sun. That makes it a Balsamic Moon, which is from 315 to 360 degrees ahead of the Sun.
For more on what Moon phases say about your life purpose and core personality, along with all the phases with their degrees, see Overview: Moon Phases.