1.  What does siege do?

A siege attacks the buildings in a city, not the armies.  There are two possible outcomes to a successful siege:  Raze and Capture.  Razing completely destroys the city, wiping it off the map.  Capture transfers the city from the attacked player to the successful sieging player.  Capture is only available if the sieging player has sufficient population to add another city in the usual manner (by settler).  If the sieging player does not have sufficient population to add another city, the only available option at the conclusion of a siege is Raze.

2.  How do I siege someone?

In order to siege a player, you need to have completed the Siege Encampment technology and have built siege equipment (catapults or the equivalent such as mangonels).  Battering rams or the equivalent such as siege hooks are NOT required in an unopposed siege.  The Siege Encampment technology becomes available at barracks level 20 and takes 4 days.  

To make siege equipment, you need to research War Machines, which requires a level 15 barracks and takes 2 days.  To make siege equipment you need siege blocks, which can be purchased on the market or built in the Siege Workshop.  It is more efficient to begin making siege equipment while studying Siege Encampment, as each unit of siege equipment takes 11 hours to build.  The more siege units you use, the faster the siege will be completed.  Fewer units can be used for smaller towns. I used 5 to take down a very small inactive town.

Once you have the siege equipment assigned to an army with a commander and have studied Siege Encampment, you're ready to siege.  To start the siege, click on the city and Send Army, then choose Siege.  In the bottom part of the Siege page you will need to select a square next to the city from which to siege.  Which square you choose is of no importance to an unopposed siege but is highly relevant to a siege that will be defended.  I leave it to the vets to explain how and why.

If the city you are sieging has troops, it may be advisable to send a separate army to Attack and wipe out the troops before the siege begins or during the siege.  This will save having to have an army sitting there with your siege troops to wipe out the army during the last phase of the siege.  On the other hand, as you successfully reduce the population of the city during the siege, some of the army may desert due to lack of tax income, and therefore the army at the end of a siege MAY be smaller than the army at the beginning. 

 In either case, it is advisable to at least scout a city before beginning a siege to ascertain the status of the army.  You may also wish to spy on the city to assess the general number and level of buildings as well as the resources available should the city be captured.

After you have done that, you sit back and wait for the siege army to travel.  When the siege has landed, it takes 12 hours to set up the camp.  When the 12 hours has elapsed, your siege engines will fire one volley each hour.  Each time they fire, you will receive a report indicating the number of hits and misses, and for hits which building was destroyed and the level that remains.

You need to reduce the city to 25% of its original population in order to capture or raze it.  For example, if a city starts with 400 population, you need to reduce the population to 100 before it can be captured.  If a city starts at 8000 population, you must reduce the city to 2000 population in order to capture it.

You receive a notification at the beginning of the siege of this target population.  When you have reduced the population enough, with each hourly report you will be given the option to Raze or (if you are eligible based on population) to Capture the city.

The final step in the siege is to send your army to raze or capture.  If you have previously cleared the troops from the city, this should be a straightforward process.

A note about walls:  Destroying the walls using battering rams, siege hooks, etc., is NOT necessary to successfully siege a city.  The main reason one would want to tear down the wall would be to reduce the defensive bonus of that army in the city, to reduce casualties in your army when you clear the city.  This is usually only necessary in an opposed siege, or possibly if there is a very large defending army in the city.  Particularly if the intention is to capture the city, it is better to leave the walls intact and take the additional troop losses.  This means you won't have to rebuild the walls after you've captured the city.

3.  What happens if I raze a city?

If you raze a city, the city is completely destroyed, including all of its contents.  If it is the player's last remaining city, a zero population city will spawn at another location on the map.  The city will have no buildings, but any research completed in the razed city will still be completed in the new city.

4.  What happens if I capture a city?

If you capture a city, the new city (or what is left of it) becomes yours, together with all the resources in the city at the time of its capture.  All research that was completed by the previous owner will remain. Mana and research points will be reset to zero.   Keep in mind that the storehouse and warehouse will have been reduced in level by your bombardment, so the resource remaining in the city maybe be much reduced.  It may be to your advantage to use raids or thieves to ensure any excess resources are not lost.

5.  Why would I want to siege someone?

This answer does not address the use of sieges in war.  In general the reasons a siege would be conducted in peace could be 1) to capture the city, 2) to raze a city in order to be able to move a non-NAP'd city within 10 squares, 3) to move another city on the city's exact location  in order to take advantage of a favorable location, 4) because the city's owner wants to start a completely new city in a different location or 5) just for fun.

And if you do meet the requirements, it should tell you if you want to capture or raze, once youve reduced the population to 25% of course.

i) Can you add siege equipment to the siege  if you want to "speed it up"? (or perhaps you                    didn't initially send siege equipment to take the the walls, and want to add it)

ii) Can you reinforce  during the siege process with  troops that will be used to battle the troops             within the city when the siege part of the operation has been completed?

If you send 2 siege armies (from 2 different cities), would the first one to arrive be considered the main siege and would that army be the one that should include the troops to take a defended city? 

Is it possible for the siege army that arrived second to make the final shot, and would that army need to include the attack troops?

You may ask why the sieging player wouldn't plan properly to start with, but there can be times when speed is of the essence.

Thanks very much.

"I'm asking for a friend"  

Sieging with multiple armies will speed up the process somewhat, but also increases the likelihood that one will "overshoot" and reduce the population below the required amount, so it should be used with caution when the intention is to capture the city.  If one intends to capture, it is strongly recommended that the siege army from the player who wishes to capture arrive some hours in advance of any other sieges, for reasons described below.

When more than one army is sieging, each army will be assigned a population at which the city can be razed or captured.  The earliest army to begin bombardment will have the highest population target.  All armies that begin bombarding after the first army will have their target population reduced based on the total population of the city when bombardment begins.  If a city begins at 10k population, the city must be reduced to 2.5k population in order for the siege army to take the city.  If a second army begins to bombard the city after its population has already been reduced to 8k, that army will have the option to raze and capture when the city reaches 2k population.

In any case, the army that is accompanying the siege army will be the army that accompanies the army on the raze/capture step.  So if the second army to begin sieging is the only army to have troops available to overcome the troops in the city, one would complete the raze/capture step using the siege page of that army.  The population will need to be reduced to the amount based on the total population when that army began bombardment.