Can you explain the detox system to me perhaps in laymans terms?

Like the immune system, which is a variety of things so is the detox system.  There is the blood, lymphatic system parts of the immune system the liver, the colon, the skin, etc.

I have heard of specific supps which are “detox provokers”, does that mean we have to provoke detox, and it doesn’t happen by itself.

Our body's are generally pretty efficient at detoxifying and /or eliminating most toxins.  If our systems were not very efficient then we would not last very long.  But sometimes we have trouble with systems either being overloaded or suppressed.

What can hinder detox activity?

Again it depends on the system.  But a few things that can affect our ability to eliminate toxins include lack of exercise, lack of flora, poor liver or kidney function, heavy intake of toxins such as herbicide/pesticide exposure or many pharmaceutical medications, low vitamin B intake and lack of water intake.

Does methylation play a role in detox, if so to what extent?

Some "toxins" can be broken down by methylation.  For example, the liver uses methylation to break down excess estrogens and in the metabolizing of drugs and some other substances.  Homocysteine, produced by the body can actually be considered a toxin, and it is dealt with by methylation.

If toxins aren’t “detoxed” what happens to them, do they get stored somewhere?

Depends on the "toxin".  Even water can be toxic to the body, which is why the body works to rid itself of extra water.  Estrogens are broken down in to metabolites that are then broken down by the flora in to inert substances that are expelled in the feces.  Uric acid is used by the body as an antioxidant, then is converted in to urea and eliminated in urine.  Carbon dioxide is used for several purposes in the body such as formation of stomach acid and the remainder exhaled.  Ammonia compounds are primarily dealt with by the liver, but some can also be expelled through the skin........

Some toxins can be stored in the body as well if the detoxification systems are overwhelmed.  The excess is normally stored in body fat.

Does detox just mean get “rid of and out of the body”?

It could be breakdown and/or elimination of the substance.

If toxins are stored, then how does the liver get rid of them, does it suck them in once it’s got a few mins spare ;)

Kind of.  If the liver is not so overwhelmed then it can work on dealing with stored toxins.  But again there are various aspects to the body's detoxification system.  Even dietary phytates, algins and pectins can help with biding and removing heavy metals.  So it is not only the body itself that helps us to detoxify.

Or do you have to provoke the toxins out of hiding so the liver can process them?

The liver has to be up to par for the liver to do a proper job of helping to detox the body.  This is one of the reasons I like bitters and B vitamin sources to help the liver function properly.

What exactly is involved in the processing of them out of the body?

Again it all depends on what "toxin" you are referring to.  Different "toxins"a re dealt with by the body in different ways.