The philosophy of a raid is to send troops into the enemy's soft underbelly and destroy his means of production (citizens). The ideal unit for this mission is the Horse Archer (HA) line at the stables for three reasons: the unit moves fast, it can fire when moving, and it can take a reasonable amount of damage.
The raider often has to accept the complete loss of his force in order to disrupt the enemy economy. If your force gets back without too many losses and can garrison to recover attrition and damage from other defenders, consider it to have been a very successful raid.
Of course, there are several things to bear in mind.
A raid should be conducted when it's least convenient for your enemy. This should ideally be early in the game, because it is more difficult to replace a citizen then than when an economy is buzzing along nicely. You have to get the enemy at the worst time for them.
This is not the only time, however. If you are about to engage in a pitched battle, consider keeping some raiding troops to the side. Send them around the sides and into his economic heartland to maul peasants while his attention is on the battle. The pitched battle has a good chance of turning in your favour if his economy cannot support troop replacement.
Set your raiders to Raid stance (three clicks of the stance button) - they will attack peasants first, military attacking them second, and economic buildings third. The goal is to disrupt the enemy economy, and peasants are the vital targets for this. Always expect to lose your raiders, and consider it a bonus if any return.
Your waypointed route should take you through known economic areas of your enemy's land - cliffs and forests are always good places to expect lumber camps or mines, along with their attendant citizens. Plotting a route back and forth around an expected or known economic site can often guarantee a good number of kills. Always try to go near rare resources - these fall very quickly to HA attacks, and the extra bonuses are immediately lost to your foe. An enemy who loses his peacocks, for example, will often find himself overpopulated and embarrassed.
Trading routes should always been watched for, as the caravans are a tasty gold bonus for you and a notable loss for your enemy.
Going too close to a garrisoned city, fort, or tower can take down quite a few attrition-damaged HAs. Attrition finishes very few HA raids by itself, but the damage is continuous on every unit in enemy territory, and the HAs are often at half strength or less by the time they enter proper combat.
Consider mixing a few other troop types in your HA raiding force. A cataphract or two in the mix can really ruin the defender's day, and it eases the production costs to your wood supply.
A small raid can be useful to dive into enemy territory and get him working to defend, but pull your guys out after a few shots and heal them before striking elsewhere.
Splitting your forces and leaving one HA in a vulnerable spot in the enemy territory will distract your foe, or even lay waste to his citizens if he fails to spot it in time. This really comes into play if you meet no attrition, but it can still be a valuable distraction even if your troops die slowly. A raiding force can be anywhere from six to sixteen (or more!) HAs, but you can cause plenty of damage over a wider area by splitting your forces.
Two small forces can be more fun that one, especially when they enter enemy territory from different sides. Repeated sallies by small forces in different locations can often keep your enemy confused.
The most important thing to remember is that raiders cannot reduce cities by themselves. Always keep in mind that they are there to remove the peasants, and that you should take their diversion as a chance to launch an assault with more conventional troops - the double punch technique, if you will.
Never even attempt to reduce partially built buildings you see on your way unless they are only a few percentage points built. If, for example, you see a partially built city on your shared border, slaughter the peasants and send in the heavy infantry to deal with the building while your HAs find more appropriate targets.
The HA changes to the scout car at the industrial age, but it is no less feasible to send a few in from unexpected directions. The attrition levels are often higher, but every increase in the forage line at the smelter will reduce attrition taken heavily.
Attrition, even at its most basic level, will shorten an enemy raid. You cannot rely on this, though. Light cavalry and its line is your best type of defending troops, though a good guide for bleeding a raiding force is a third of the raiding force's numbers. If you are forced to use foot troops to defend against an early age raid, only use archers. They are the only troops with enough range to hurt the raiders, and anything else will be arrow fodder for HA.
Forts are too expensive to dot around the landscape, though they can guard the occasional route into your territory and damage raiders heavily. Towers are good, since you can slip your peasants into them in the event of a raid. They do get expensive, and you do force yourself into a defensive mindset by doing this (you can only win by attacking), so consider just placing the occasional one here or there and place them near valuable resources (between a lumber camp and mine, for example).
The AI will usually bell all its citizens into cities and towers when attacked, but it is a severe blow to your economy to do this. If at all possible, just select those peasants in the direct line of fire and garrison them, letting them out as soon as the danger has passed.
As always, your best defence is knowledge of the enemy troop disposition. Spies are not fast enough to bribe raiding HAs, but they can let you know that they are coming.
*to be updated*
Rapscallion with assistance and commentary from War - this will be updated at some point.