How does new shield system work?

After the upgrade I can't figure out how the new shield system works. I have the option to discard the shield, and I notice I have a new potion in the inventory.

More importantly, I got attacked (and lost) twice in a short amount of time and don't have a shield. When do you now get shield?

Solution 1:

The shield system has been changed in the following ways as part of the 10/12/2015 update:

• Shields are no longer awarded on destruction of town hall. Also, your town hall holds much more loot (1/5 of total). As such, trophy farming has been massively nerfed.
• You get a free 12 hour shield at 30% destruction
• You get a free 14 hour shield at 60% destruction
• You get a free 16 hour shield at 90% destruction
• The attacker must use at least 1/3 of a full army for their TH level¹
• Attacking through a shield removes 3hrs on first attack, 4 hrs on second attack, 5 hrs on third, etc (attacking no longer removes it entirely). Shield time is deducted on attack (i.e. when you drop a troop), hence you can search for bases without draining your shield.
• Shields can now be dismissed at any time by clicking the red minus sign on the shield icon.

Another shield-like mechanic called the Village Guard was also introduced in this update.

• The village guard acts like having the app open and online. You cannot be attacked and you can attack as many bases as you like without depleting it. Note you can dismiss it at any time, like shields.
• You can buy 2 hrs of village guard once a day in the store for 10 gems.
• Buying a shield from the store will remove any active village guard.
• Between 30 min and 4 hrs of village guard is automatically activated after a shield wears out. The time given scales with league level.²
• Any attack which does not result in a shield awards free village guard depending on your current league level (explained below)
• The village guard counts towards the Personal Break timer

You may be asking: what's the difference?

• Village guard lasts for a short period, while shields last for a long period
• You can attack through both the shield and the village guard, however attacking through a shield removes time
• Free village guard time scales depending on league², however shield time is the same for all players

Footnotes

¹While the wiki and other sources suggest that the shield is only awarded when at least 1/3 of their troops are deployed, the official developer forum posts say that:

Attacks of less than a 1/3rd maximum army capacity (based on the Army Camp, Spells and Hero capacity of the defender's Town Hall level) will not grant any shield

²Free village guard time awarded upon shield expiry:

Master I League players and below: 30 min

Champion League players (all levels): 1 hour

Titan III League players: 2 hrs

Titan II League players: 3 hrs

Titan I and Legend League players: 4 hrs

Sources

From the Dev's Desk: Shields - Part I: Attacking and Defending

From the Dev's Desk: Shields - Part II: Village Guard and Personal Breaks

Solution 2:

At 30 percent damage, you will get a 12 hour shield. At 60 percent, the shield extends to 14 hours. Finally, complete destruction means a 16 hour shield. Shields can be removed and be replaced by a 15 minute Village Guard. Attacking through your shield will deduct 3 hours the first attack, 4 more hours the next, then 5 hours after every other attack until you have no shield left.

Village guards are very short, allowing players to be safeguarded from all attacks but will be instantly removed if attacking. More info coming soon.

Note: A shield deduction will be applied after you start a battle, so if you don't place a troop, nothing will happen.

Solution 3:

The new shield system has been described in detail in these posts by Supercell staff in the Supercell forums: From the Dev's Desk: Shields - Part I: Attacking and Defending, From the Dev's Desk: Shields - Part II: Village Guard and Personal Breaks (Most of the info in those posts are also in this answer by angussidney).

Just would like to add that there has been significant changes to the mechanics behind shields and personal breaks as per the 2015-12-17 update:

• Personal Break online-time limit has been increased from 3 to 4 hours
• Personal Break limit now fully resets when being 15 minutes offline without Shield or Guard (was 30 minutes)
• Personal Break limit extensions increased to 30 minutes (was 15 minutes) after taking a defense without shield or getting kicked out without being attacked
• Free Guard when Shield expires has been increased for all Leagues:
  • Titan I / Legend: 4 hours Guard (was 3 hours)
  • Titan II: 3 hours Guard (was 2 hours)
  • Titan III: 2 hours Guard (was 1 hour)
  • Champion (all levels): 1 hour Guard (was 30 minutes)
  • Below Champion: 30 minutes Guard (was 15 minutes)