A couple of possibilities exist.  Prior to forming a planetary nebula,
a low-mass star (i.e., one with a mass similar to that of the Sun)
forms a red giant.  Planets close to the star are engulfed in the
expanding star, spiral inside it, and are destroyed.  In our own solar
system, Mercury and Venus are doomed.

As the star expands to form a red giant, it also starts losing mass.
All stars lose mass.  For instance, the Sun is losing mass.  However,
at the rate at which the Sun is currently losing mass, it would take
over 1 trillion years (i.e., 100 times longer than the age of the
Universe) for the Sun to disappear.

When a star enters the red giant phase, the rate at which it loses
mass can accelerate.  The mass of a star determines how far a planet
orbits from it.  Thus, as the Sun loses mass, the orbits of the other
planets will expand.  The orbit of Mars will almost certainly expand
faster than the Sun does, thus Mars will probably not suffer the same
fate as Mercury and Venus.  It is currently an open question as to
whether the Earth will survive or be engulfed.

The orbits of planets farther out (Jupiter, Saturn, Uranus, Neptune,
and Pluto) will also expand.  However, they will not expand by much
(less than double in size), so they will remain in orbit about the Sun
forever, even after it has collapsed to form a white dwarf.

(Any planets around a high-mass star would be less lucky.  A high-mass
star loses a large fraction of its mass quickly in a massive explosion
known as a supernova.  So much mass is lost that the planets are no
longer bound to the star, and they go flying off into space.)

As for the material in the planetary nebula, it will have little
impact on the planets themselves.  The outer layers of a red giant are
extremely tenuous; by terrestrial standards they are a fairly decent
vacuum!