1st House
The first house is the house of self. Its cusp is called the Ascendant: the degree rising in the east at the moment of birth, and it is what shapes the first impression a person makes.
What the House Rules
The first house describes how a person walks into a room: appearance, manner, pace, style of reacting. It is the "packaging" of the personality, which can differ greatly from the Sun sign.
It also covers physique, health in the sense of overall vitality, and the way a person starts anything new.
Planets in the House
A planet in the first house noticeably colors a person's manner: Mars brings sharpness and directness, Saturn reserve and an apparent sternness, Venus softness and outward attractiveness.
The Sun in the first house strengthens the match between inner and outer self: the person is roughly who they seem to be.
Sign on the Cusp and an Empty House
The sign on the Ascendant changes roughly every two hours, so calculating the first house requires an exact birth time. An hour's error means a different Ascendant. You can calculate it with the Ascendant calculator.
An empty first house (with no planets) is perfectly normal: there are ten planets and twelve houses, so some houses are always empty. It is interpreted through the sign on the cusp and that sign's ruler.