Well Sling you asked for it as an honourary Australian...

"The Foreigner's Guide to Vegemite
The story of VegemiteVegemite is a registered trade mark, and due all of the protection that it receives under the law, but it is also part of Australian culture: it is celebrated here as part of that culture.
We Australians eat Vegemite in large lumps or small dollops, but mostly in large lumps. If you can see the thing the Vegemite has been spread on, then there isn't enough. Of course, if you have never eaten Vegemite before, you may need to consume it in slightly smaller amounts until you get used to it.
This account is in four parts:The history of Vegemite's inventionThe biochemistry of making VegemiteHow to make a Vegemite sandwichHow to make a Lamington

The history of VegemiteFirst, here is the official history of Vegemite, as supplied to me some years ago by the manufacturer, who states that Vegemite is as much part of Australia's heritage as kangaroos, Dame Nelly (sic) Melba and Holden cars, and adds that since the early 1920s, Vegemite has fought along the ANZACs in World War II (it's pugnacious stuff, apparently, but a bit slow, given that the ANZACs stopped fighting in 1918!), but then they get past the flack's flawed imagination to this account, edited only to remove bizarre punctuation and a plethora of apostrophes. The strained syntax is theirs, not mine!
Vegemite dates back to 1922 when the Fred Walker Company, which became Kraft Walker in 1926 and Kraft Foods Limited in 1951, hired a young chemist to develop a spread from one of the richest known natural sources of the vitamin B group -- brewer's yeast.
Following months of laboratory tests, Dr. Cyril P. Callister, who became the nation's leading technologist of the 1920s and 1930s, developed a tasty spreadable paste.
Dr. Callister had filled his part of the contract, but Fred Walker was still to name his spread. So Walker turned to the Australian public for help and conducted a national trade-name competition, offering a tempting 50 pound prize pool for the winner or winners.
How the fifty pounds was distributed is unknown, but in 1923 Fred Walker named and launched his product under the Vegemite brand. Even though Dr Callister's invention has proved to be a formula for success, success was not instantaneous. Fred Walker persevered for 14 years before his beloved product finally gained acceptance and recognition.
When Australians first heard about Vegemite, a thick, dark English spread dominated the spread market and Australians were reluctant to try Fred Walker's locally made product. Hence, poor sales performance resulted in Vegemite being re-named -- four years after its launch -- in 1928.
To compete with the opposition, Fred Walker re-launched Vegemite that year as "Parwill". "If Marmite . . . then Parwill" was the rationale behind Walker's strategy to carve a niche in the market for his concentrated yeast spread.
Walker's 'creative' play on words fell on deaf ears and "Parwill" failed. When Walker went back to the drawing board, he finally realised that the Vegemite brand would work. All he had to do was stimulate consumer trial.
He achieved the objective. In 1935 a vigorous 2-year coupon redemption scheme was launched whereby a jar of Vegemite was given away with every purchase of other products in the Fred Walker company range. Australians tried the product and loved it. Vegemite was well and truly on the road to success.

Here endeth the history lesson. Here beginneth the biochemistry lesson, in MY words:Brewer's yeast is a good source of vitamin B, but live yeast tastes boring, it is poorly digested, and it can even strip vitamin B from the gut. Inactivated yeast lacks the disadvantages, but is still bland. The answer is autolysis: using the yeast's own enzymes to break it down.
Spent brewer's yeast is sieved to get rid of hop resins, and washed to remove bitter tastes. Then it is suspended in water at a temperature greater than 37 C with no nutrients: the yeast cells die, and vitamins and minerals leach out. Then the proteolytic (protein-splitting) enzymes take over, breaking the yeast proteins down into smaller water-soluble fragments, which also leach out.
The yeast cell membrane is unruptured during this time, and can be removed by centrifuging. The clear light brown liquid is then concentrated under a vacuum to a thick paste (the vacuum helps preserve flavours and vitamin B1, thiamine). It is seasoned with salt, and a small proportion of celery and onion extracts to increase the palatability.
Vegemite is sold in a range of sizes up to 910 gram (2 pound) jars, and in bulk in giant tins which must contain about 5 kg of the stuff. Only sissies buy anything less than a 227 gram jar.

Making a Vegemite sandwichIn my experience, their next question is: how do you make a Vegemite sandwich? And a Lamington? Here, ready to cut and paste, are complete answers:
To make a Vegemite sandwich, you collect some grain, grow it and improve the stock for about 10 000 years, grind the seeds to make flour, mix into dough, knead, add yeast, set aside, bake in a greased tin in a medium oven, and slice. This is called "bread".
Oh yes, and to slice the bread, you need a bread board, made of wood. As a general rule, the best place to get wood is from trees -- the wood from sheep, for example, is much too fibrous, and bits keep getting caught up in the bread.
I can send you a recipe for making "butter", but you can also buy this in specialty stores called "supermarkets", from "super", the Old Hittite word for yaks' knees (they used to treat them with butter when they creaked). You will need some butter.
You also need a knife -- let me know if you need to know how to make one -- I believe that the good people of Texas have something similar, that they call a Bowie. Steel is generally best, and frozen mercury is not much good at all. The only wooden knife I ever used tended to merge in with the bread board, and be hard to find.
Anyhow, then you spread the butter on the bread with the knife, add Vegemite in the same way, slap two slices together, and you have a Vegemite sandwich. What could be easier?
Now perhaps you would like to see what the children at one of our local primary schools think about Vegemite. Try the Elanora Heights Primary School Vegemite page for size and taste.
LamingtonsLamingtons are just about as easy to make as Vegemite sandwiches. You buy them from the Lamington shop.
We bring our children up on these two delicacies, so as you can see, it is really easy for us to explain them in simple terms that foreigners can understand.
How do the lamington shop people make them? Well, first you have to know that Lamingtons were invented as a way of rejuvenating stale sponge cake. So if you are going to make genuine country cake-shop Lamingtons, you need a nice solid sponge cake, cut into cubes.
Next, you roll the cubes of cake through some chocolate icing, and then into a tray of desiccated coconut, so the chocolate-covered cake looks as though it has a terminal case of dandruff.
Some people slice the Lamington, and smear cream in between, but this detracts from the main flavours.
To the best of my knowledge, nobody puts Vegemite in a Lamington or dunks them in beer -- the TimTam Suck is bad enough, but I refuse to discuss that on grounds of good taste.
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There you go Sling...