What are metatables, and how to use them?

The analogy that I'd heard once before and tend to think of as a good starting point is that they're like events, but for tables.

Each metamethod is unique, but once you get the idea for one of them the rest should come pretty easily.

Here's an example of using the __index and __newindex metamethod which only fire when indexing a position thats value is currently nil.

local someTable = {"cat", 7, "apple"};
local someTable2 = setmetatable({}, {
	__index = function(t, k)
		-- someTable2 is always empty so this metamethod should always fire
		if (type(k) == "number") then
			k = k + 1; -- now the table is zero-indexed b/c 0 becomes 1 and so forth
		end;
		return someTable[k];
	end;
	__newindex = function(t, k, v)
		-- add new indexes to someTable with adjsuted index
		if (type(k) == "number") then
			k = k + 1;
		end;
		someTable[k] = v;
	end;
});

print(someTable2[0]) -- cat
print(someTable2[1]) -- 7
print(someTable2[2]) -- apple

someTable2[1] = false;

print(someTable2[0]) -- cat
print(someTable2[1]) -- false
print(someTable2[2]) -- apple

This page gives an example of all the metamethods in use, hopefully that's enough to get you started.