If photons travel at the speed of light than due to relativity they must experience no time frame in which to be destroyed in the first place so they must be immortal which is silly. So, clearly I am misunderstanding something.
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"Photons experience no time" is a conclusion drawn from taking the limit of time dilation as $v$ approaches $c$. This transformation never gets you to light speed, i.e. never represents a massless particle, only gets asymptotically closer. Taking that same limit, length contraction causes distances to reduce to nil. A particle moving at the speed of light using this treatment would experience no time, but also no distance, when "traveling" from one atom to the next.
Obviously all of the above indicates that the process of taking the limit of a Lorentz transform as an actual value fails us, because it results in a singularity. Since we observe that time passes and distances exist, we can't apply the conclusions of "light experiences no time" and "light experiences no distance" to reality. In fact since we can measure the speed of light we can throw out those conclusions experimentally as well, since a finite speed requires both finite distances and finite times.
So the question of "how can a photon be destroyed" is rather simple: after being created by some process, the photon travels some distance over a period of some time and is destroyed by a similar process.
Asher
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Photons are created and destroyed (they're usually thought of as packs of energy which are emitted and absorbed by other particles, as Anders pointed out) independently of what happens to them between those events. As they move very fast, any proper time interval for them is close to null. Notice that this doesn't mean they're immortal, this means that any two events in their lifetime will occur to them at the same moment. Those possible events include their "birth" and "death".
For a more detailed explanation, see David Z's answer on this question.
Edit: you might be interested to know that it has been argued that photons could indeed have a tiny mass, which would imply that their lifetime is constraint to some finite value.
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Well photons is basically made of electromagnetic radiation basicly it is pure energy so it is not made of quarks that bounce around inside a atom producing gravity and time dilation so that's why it still experiences no time dilation also this particle is a point particle it doesn't feel the effect of the 3rd dimension that we live in it is a 0 dimensional object but as this particle is still around it slowly loses its energy so adventually it would lose so much that it adventually it just kinda fades away/breakes apart back into energy
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you can't physically destroy a photon but when a photon is moving through free space it looses energy over time atoms also can assorb a photon and take some energy away but as a photon looses its energy it would start breaking apart until there is nothing left