How do I recover my old Clash of Clans (COC) game save & base?

If you are moving from iOS to Android, there are instructions in the Device Linking Guide provided by SuperCell:

VERY IMPORTANT NOTE: Play through the tutorial on the new device and use link BEFORE reaching Town Hall level 4 and before making in app purchases. If you need further assistance or experience any issues with linking your devices, please contact player support via the in-app reporting feature in the in-game settings menu! You'll find it under the Help & Settings option.

In order to transfer your village between and iOS and Android device, it needs to be connected to Game Center/Google+. You can verify the Game Center connection on iOS by logging into Game Center and opening the game from the Game Center's 'Games' tab. For Android, open Clash of Clans and connect your village to Google+ in the in-game settings by clicking the Google+ sign in button.

Everything verified? To move your village between your devices follow these steps:

• Open Clash of Clans on both your Android and iOS devices (source device and target device).
• Open the in-game settings window on both devices.
• Press the 'Link a device' button.
  
• Select OLD DEVICE on the device you would like to move your village FROM
• Select NEW DEVICE on the device you would like to move your village TO
  
• Select which type of device you want to link your village TO. If you are linking your village from an iOS to an iOS device, use the Game Center User Guide. If you are linking your village from one Android device to another Android Device, try out Google Play Guide located here: Google+ User Guide.
  
• STOP!!!! Before you proceed, please make sure you have played through the tutorial and not made a purchase before TH4. Read the VERY IMPORTANT NOTE located above.
• Use the device code provided on your OLD DEVICE and enter it on your NEW DEVICE. You have a 5 minute window of time before your code is invalid!the other, your village will be on both devices.
  
  
• After you have successfully copied the village transfer code from one device to the other, your village will be on both devices.

If you connected your Google Account before playing, you can just simply connect it again and it should automatically continue where you left of.

If you didn't connect your account beforehand, enjoy playing from the start!

If you know the name of the old village, you can recover your village that way.

Taken from an article on cocland.com and one on Clash of Clans Wikia:

• In Clash of Clans, go to Settings -> Help & Support.
• Tap on the send icon to the right.
• Give as much detail as possible as you can about your old village. At the very least, you'll need the name of your old village and new village as well as the name of your clan. If you can, provide additional details. Some additional details that will help:
  • the level of the two villages
  • the level of the town halls
  • when you started playing the old village
  • when you last logged into the old village
  • a screenshot of the old village

If the CoC support staff is able to find your village, they'll send you a code to help you recover it. The Wikia aticle recommends that you do not surpass Town Hall level 4 in the new village as it may make recovery more difficult.

If you were playing on an android device and you linked your account to Google+, you can simply log back in on the same account and recover your village instantly.

Note: This assumes you are using some form of emulation service for Android (BlueStacks)
This game does not support backed up saves games using Google Play Games. Therefore, your Google Play account does not have a backup as a result of logging into your Google Account.

Right now, their forums is down, so you would need to contact them directly for help.

I'm sorry, as we are not Supercell, we most likely cannot help you with this.

The next thing you should do is contact Supercell directly. This article on their support page might be a good starting point.

It does say to contact them in-game (via settings > help), but I cannot find any option to contact Supercell. It may only be available to newly started games, so make sure you check your device.

Good luck getting your village back!