The fixed stars are the oldest layer of astrological practice and the one furthest from the popular image of it, since they have nothing to do with Sun signs and everything to do with specific points in the actual sky.
They are called fixed to distinguish them from the wandering stars, the planets. In practice astrologers work with a small number of bright and long-observed stars, each held to carry a distinct nature: Regulus in Leo, read as royalty and honour with a warning about downfall; Aldebaran in Taurus and Antares in Scorpio, opposite each other and both read as martial; Spica in Virgo, read as the most benign point in the sky; Sirius, the brightest star; Fomalhaut; Algol in Perseus, the demon's head, which carries the darkest reputation in the tradition and is an eclipsing binary whose brightness visibly dips every three days.
The natures are described in the tradition through planetary blends, a star is said to be of the nature of Mars and Jupiter, or of Saturn and Mercury, which is a convention going back to Ptolemy and is how the tradition transfers meaning from a familiar vocabulary to an unfamiliar one.
The technique is almost entirely conjunction. A star is read when a planet or an angle of the chart falls within a degree or so of it in longitude, and the star is then held to sharpen, elevate or darken whatever it touches. Some practitioners work by parans, a more demanding method using the star's rising, culminating and setting relative to a planet on the day of birth, which takes latitude into account as simple longitude does not.
Orbs are tight by tradition, often a single degree, which makes fixed-star work a matter of exact placement rather than general tendency.