Moran's Index is a weighted index. It's hard to write the equation here but I uploaded a pdf with the example calculations.
Essentially you want to know if the area you are looking at has areas that are similar and as you move away from that area does the similarity get stronger, weaker, or it doesn't matter.
Moran's Index runs from -1 to 1.
A negative spatial autocorrelation would indicate that things close together tend to be more dissimilar than things that are further away.
A positive spatial autocorrelation would indicate, as Tobler's Law says, that things close together tend to be more alike than things further away.
Zero spatial autocorrelation would indicate that it doesn't matter, that you can't expect things close to be more alike than things further away.
Do a search for Moran's Index Calculation for the formula and sample solution.