Skyrim:Civil War

You will be asked to take sides in the Civil War being fought between the Imperial Legion and the Stormcloaks (a historical description of which may be found here). You can only choose one side.  Either choice allows you to start a series of quests, during which various battles of the Civil War are fought, ultimately resulting in your chosen side taking control of Skyrim. The overall quest arcs for the Imperial Legion and Stormcloaks are similar, and allow you to unlock the same achievements.
  
Choosing Sides
You are first asked to choose sides shortly after you escape your near-execution and the subsequent dragon attack during the Unbound quest, at the point when you choose whether to enter Helgen Keep with Ralof, a Stormcloak, or with Hadvar, an Imperial soldier. However, this choice only determines which side you will be first asked to join. 

After escaping the Helgen keep, your chosen companion will suggest that you join their side, adding the corresponding quest to your log. You can make a choice to accept the suggestion or you can postpone it. If you do make a choice, you can later change sides. While exploring Skyrim, you will fairly often meet soldiers from both sides, who will ask you to join their side if you have made no choice, or if you belong to the opposite side.

To join an army, you need to go to that army's base to join (in Windhelm for the Stormcloaks, or in Solitude for the Imperial Legion). If you have not initiated a quest to join either side, you can simply travel to either base and trigger the quest by speaking to members of the leadership. Both sides have an initiation task that you must first complete before you are inducted into the faction. Even after you are formally inducted, you will have yet one later chance to change sides. You will also be given a set of armor. Although you are not required to wear the armor, wearing the opponent's armor can result in your being accused of being a spy; ironically, this dialogue stops once you have joined one side or the other. Another implication of joining a side is that the other side now considers you an enemy. For example, if you are a Stormcloak you are no longer welcome in Imperial Camps, and after a warning, will be attacked by Imperial soldiers if you do not leave immediately.

If you join the Imperials, the second quest that you receive in the Imperial questline will be The Jagged Crown (Imperial), and if you join the Stormcloaks, the second quest that you receive in that questline will be The Jagged Crown (Stormcloak). At the end of this quest, you have a final opportunity to keep or change sides in the Civil War.

Quests
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Notes
This questline is put on hold during the ceasefire negotiated in Season Unending; Civil War quests are unavailable until after the Main Questline is completed.
Leftover dialogue, markers, quest updates, and other evidence suggests that at one time the game's developers intended the Civil War to be much more dynamic and complex than it currently is. Taking a hold would have involved capturing the outlying villages and/or points of interest as well as completing the regular missions. In addition, sieges like those seen during Battle For Whiterun and the final two battles were intended to occur with each hold capture. On top of this, the opposing side would actively participate in the war, which would have forced players to play defensive as well as offensive missions. Finally, it would have been possible for the opposing side to lose their main capital yet still have other holds, meaning the final battle may have taken place elsewhere (for example, for the Stormcloaks the final battle could also have taken place in Markarth, as well as Solitude.)
In addition to the Jagged Crown quest, you were also at one time able to defect to the other side by favoring the opposing side during negotiations in Season Unending.
An alternate method of completing any quests requiring you to take over a fort is to attack and defeat the local Jarl. Doing so is recommended in the event that the fort's defenders fail to spawn due to bugs. The quest will be marked as complete once the Jarl is on their knees. However, if the quest is completed this way, the guards and soldiers in the hold may not be replaced by guards and soldiers of the opposite faction. The Jarl and their court may not go into exile, nor will their replacements step forward or return from exile. Further bugs have also reportedly been triggered in this way.
Even after finishing the war, a lot of people will discuss it as if it is ongoing, and the events in the Dark Brotherhood questline that relate to it do not change in any way.

Achievements
The same achievements can be obtained regardless of which side you choose. Three achievements (50 points; 2 Bronze and 1 Silver) are unlocked by the Civil War quests

This is unlocked when you complete either the Joining the Stormcloaks or Joining the Legion quest.

This is unlocked roughly halfway through the Civil War.  On the Stormcloak side, you must complete The Battle for Fort Sungard.  On the Imperial side, you must complete The Battle for Fort Greenwall. Note that both of these quests are optional and may be skipped depending on the results of Season Unending, which will cause you to miss this achievement.

This is unlocked once Skyrim has been liberated/reunified.  On the Stormcloak side, you must complete Battle for Solitude.  On the Imperial side, you must complete Battle for Windhelm.