In many modern Western astrology guides, the chart ruler means the ruler of your rising sign. It is one way to follow a connection in a birth chart. The name does not mean that a chart symbol runs your life.
Find the rising sign
Look for ASC on your birth chart and note the sign at that point. You need a reliable birth time and birthplace as well as the date. A guessed time may give you a different rising sign.
Match the sign to its ruler
If Leo is rising, its ruler is the Sun. In this common method, the Sun is the chart ruler even if it is in a different sign.
Look at the ruler in the chart
You can then check the Sun's sign and house in the same chart. Astrologers may use those positions to add context to the rising sign. One chart placement does not settle your personality or predict what will happen.
A few common questions
Does chart ruler always mean the ruler of the rising sign?
No. That is a common modern use. Some traditional methods choose an overall chart ruler by other rules, so check which method a source means.
Sources & further reading
Astrology sources describe their own traditions and methods; they do not establish predictive accuracy. The writing exercises are original Lodestar editorial material.