If you wanted to compose an index consisting of 100 stocks (and assuming for the sake of this example that you wanted the initial value of the index to be 100, though you could just as easily start it at some other number like 1,000 by multiplying by an appropriate multiple) Divide each stock's current price by its price on the first day you created the index and then add it all up (which would give you an answer of 100 of course). Chart this over time and you'll see the performance of that basket of stocks compared to where the average was at the date of inception.

That is how you would create an index that isn't weighted to market capitalisations. Market capitalisation weighted indexes are only slightly more complicated to create.

If a stock represents 5% of the market you are trying to create an index for, multiply its price by a factor that would equal 5% of the starting value of the index. Just say a stock was $6.50 and was 5% of the market, and you wanted to create an index starting at 1,000, you would need to multiply the stock price by (1,000 * 5% / $6.50) = 7.692. You'll need to perform a similar calculation on each of the stocks you want in your index.

Every now and then you'll want to change your multiplier for each stock to reflect changes in market weightings. They do this regularly with real indexes like the All Ordinaries. This is what they mean by stocks getting "reweighted" in an index, which leads to a flurry of activity from fund managers who update their portfolios to reflect the new weighting given to the stock.

A variation on market weighted indexing is a "free float" index. Instead of calculating the market capitalisation of the stock as such, they calculate the capitalisation of the stocks that are traded on the market (as opposed to closely held by the company and associates). For example the free float value of some companies such as Newscorp is much less than the market capitalisation of the company, because a large chunk of Newscorp shares are owned by the Murdoch family.

Apart from price indexes, it is also possible to calculate "accumulation" indexes, which track not just price but also dividends.