Imagine that you have a laser and in front of it you placed barrier with two slits. Because of Wave-Particle duality light behaves like a wave (When we don't observe it) which is travelling at speed of light. When you will light up(turn on) the laser, on screen you will see interference pattern(Interference is phenomenon when two waves meet each other), to explain interference imagine a two waves that meet each other. At some places this waves will cancel each other out and you will get 'black dots'.
When two waves which look like this meet they cancel each other out.
Here is an animation that shows what will happen when two waves meet each other:
Same happens with light. When wave passes through a slit it 'creates new wave' and when wave passes through two slits it 'creates two new waves' which meet each other (in other words: interferene) and on screen you will see interference pattern.
Here is sample image of double slit experiment:
When sunlight passes through one slit it 'creates new wave' and that wave passes through two slits. This two slits 'make two new waves' and when this two waves meet each other they cancel each other at some points (interference) (To see simulation of interference you can use this or this). But According to Quantum mechanics when we will 'observe light' (We will know in which slit photon passes through) we will 'collapse wavefunction' (in other words interference pattern will dissapear). to 'collapse wavefunction' you can simply add polarizators at the both slits.
EDIT: So your question is how can one photon interference with itself. It happens because of Wave-particle duality (for example light sometimes behaves like a wave and sometimes like a particle), When we don't observe light it behaves like a wave but when we will put detectors it will behave like a particle. now in order to get interference pattern we must have two waves that will meet each other. Because of 'not observing light (It means that we don't know path of a photon)' light behaves like a wave. When we will place barrier with two slits, that 'one' wave of light will be split (Imagine how two waves of water will behave when you will place barrier with two slits in from of them) in two parts and when this two parts will meet, they will cancel each other at some points (in other words interference) and then it will hit detector screen, but according to Wave-Particle duality when we will observe light it behaves like a particle (photon). So we can't say that where one photon will hit screen, we can say that what is probability that after observing we will find photon at some place. Because waves cancel each other at some points(interference) probability of finding photon after observing becomes zero at points where two waves canceled each other. So after shining laser (shooting photons) through a double slit we will get interference pattern.
Same happens with electrons:
(Interference means that two waves meet each and they cancel each other at some points. In order to make one light wave to interference with itself you have two slit it in two parts which will interference with each other)