I Need Brian Cox.

[Pumpkinstew]

Um, well, if you're happy with idea that matter and energy are equivalent that's always a good place to start.
Then you have to start thinking of particles as not being finite. Instead they're little bundles of waves which have a probability density which localises the vast majority of that energy in that one region of space (and time).
This wiki entry is a bit formal but has a useful graphic

That gets you to the interference pattern (wavelike behaviour) being created by particles. And other phenomena such as quantum tunnelling and Hawking Radiation.

Then the thorny bit - how does observing the wave/particle cause it to behave more like a particle than a wave? Especially as it may have passed through the slit you aren't observing!
There isn't a definitive answer that I know of. Relational Quantum Mechanics has a bash at explaining it. But really it comes down to saying the same thing - by observing the quantum system you force it into a state instead of a range of possible states at the point in time and space when it is passing through the slits. Schrodingers equation is time and space dependent remember.
Importantly though in RQM the observer becomes part of the quantum sytem, and different observers may see different, but still correct, outcomes because the equation continues to evolve with time.

It's worth pointing out though that various detectors and particles have been used in the double slit experiment and the level to which the interference pattern is disturbed varies. this strongly suggests that the fundamental interation between the detector and the wave/particle at the point in space time at which it passes through the slits is what varies the strength of the interference pattern.

The QM I did at university is a hazy and distant memory though and i may have gotten totally the wrong end of the stick. If you were still in Exeter I could have suggested a professor who would know for sure. I may have an old textbook at work still. I'll have a thumb through it tomorrow and see if it becomes any clearer.