This is normally done by having a year that corresponds to a cycle of seasons and a month which corresponds to a lunation so that the day of month indicates the moon phase and the month of year indicates the season. Also there is usually the additional requirement that the year has a whole number of months, in which case most years have 12 months and the other years have 13 months.
The Hebrew calendar and the Chinese calendar are lunisolar. The Islamic calendar is not lunisolar because its date does not indicate the season and the Gregorian Calendar is not lunisolar because its date does not indicate the moon phase.
See "Month" for more about how many months there should be in a year.