Reading Player Scores (and a disclaimer)…
Good scouting and reading the opponents score can give a lot of information about the opponents strategy.  Unfortunately, Ensemble Studios does not offer a method to read the economy and military scores separately (only the total).  A third party program must be downloaded and installed in order to make this work.  I included this guide to show the score theory, not to promote third party software.  As a matter of fact, I look down on anyone taking advantage of third party software when their opponent does not have it.  If both parties have the same tools, then I do not see an issue and it adds to the strategic depth.  Never play a strategy game with an unfair advantage.  Announce before the game what third party software you have installed, stick to playing with friends, or risk being banned when caught.
How Score is Determined
Essentially the score is the value of what the player currently has.  That means resources in the stockpiles as well as the buildings, units, and technologies.  Every 100 resources make for one point.  Units or buildings that are killed or destroyed no longer count towards a player’s score.
In the post game, the military and economy scores can be viewed separately.
These are calculated the same way the total score is, just split into two categories.  Players get one point for every 100 resources in the stockpile or invested in economy (villagers, buildings, and technologies).  military works the same way.  The cost of all military units, buildings, and technologies make up the military score.  The mini-map filters use the same categories as the score.
This can be enormously valuable information in game, so get a user interface with an economy / military score option and learn to use it.  There are many different UI's available but be careful.  Some people consider this cheating and is grounds for being banned.  Check with Ensemble first.
This means that it will remain unknown if someone has started to age up based on their economy score.  The resources have simply been reinvested and are still counted as part of the score.  However, military units, and technologies do not appear to count until they are finished being created or researched.  Military buildings still show up as part of the military score as soon as the amount is deducted from the economy score.  Thus when the enemy has spent a lot on military, it will be obvious.
The scores types for all units and techs can be seen in the proto and technology tree files.
Things to Watch Out For
Economy score does not seem to include extra economy score for trading posts that are set to gather resources.  Depending on the map they can easily be counted as 10 points.
Native trading posts are counted as economy, not military.  Do not expect to be able to tell the difference between a fast fortress and a native rush by looking at the score.  There is still no substitute for scouting.
Wagons do not count until the foundation is placed.  Forts are worth 11.
Numbers round down.  A 250 wood barracks shows up as a military score of 2 if that’s the only military present.  A barracks and an outpost (250 wood) still make for 5 military points.  A war dog (75 food) alone is zero but with an outpost comes to 3.
When the enemy (or yourself) builds a trading post, either a dot or an arrowhead will appear below the players name (above the players score) depending on whether the player built on a Native Trading Post or a standard TP.  This is very useful in determining if a player is going to rush, especially a Native American rush.
Putting the Knowledge to Use
Military score is useful at showing what strategy the enemy is using.  Combine scouting with frequent glances at the score to guess the enemy's plans.  The most simple is if any military has been made but there are subtleties that can be just as valuable.
Consider someone who builds a stable and trains cavalry compared to a cavalry shipment.  A 300 wood stable will result in -3 economy and +3 military as the foundation is placed and then the economy score will drop by 10 when 5 hussars are queued.  Then the military score will increase by 10 as the hussars pop out shortly thereafter.  Someone who has a single outpost will have a military score of only 2 and then 8 as the 3 hussar shipment arrives.
This article, "Reading Player Scores" was originally written by "Flammifer" (and edited by myself) from Age of Empires III Heaven.