TL;DR: En Sabah Nur was born with the ability to alter his body on a cellular level.
In the comics, the being later known as Apocalypse was born with a single mutant power - to control his body on a cellular level. Once he learned to control this ability, however, it granted him a variety of useful abilities:
- Near-instant healing
- Limited shape-shifting
- Enhanced strength and speed
- Immunity to poisons
- Control of his own aging, making him essentially immortal
He also has a genius-level intellect, but it's unknown whether this is because of his power, or in addition to it. The outward sign of his mutation is light gray skin and blue lips.
While a young adult, roughly in his mid-twenties, En Sabah Nur obtained access to a crashed alien vessel, possibly Celestial in origin. This technology granted him access to a plethora of other "powers", including the blue armor he is most often seen wearing as well as telekinesis and energy manipulation.
In the Fox films franchise, I was unable to find an explanation of his original mutant powers. We do see a teenaged En Sabah Nur in the after-credits scene of "X-Men: Days of Future Past". In that scene, he appears to be moving blocks using telekinesis or some similar ability.
Later, in "X-Men: Apocalypse", he seems to demonstrate the ability to affect matter on a molecular level, trans-mutating one substance into another (flesh into crystal, for example). Whether this is the same ability he used to move the blocks around, though, is never mentioned.
As for stealing the abilities of other mutants, that appears to be a function of the alien technology he obtained. In the latter film, we find that Apocalypse's "temple" is actually
an alien ship shaped like a pyramid
and it is the device and/or "altars" located there that allow him to do that. This same process seems to also grant him the ability to transfer his consciousness into a different body.
Note that in the scene mentioned above, En Sabah Nur is elderly. His priestess demonstrates the young mutant's ability to heal instantly, then says to Apocalypse "Now you will rule for eternity, my lord." It's unknown if that is En Sabah Nur's original body (the elderly one, that is). However, the fact that he both aged and got the healing ability from someone else, would seem to indicate that his initial power in the film was different from the comics.