This document shows how to create an offline wallet that holds your Bitcoins and a watching-only online wallet that is used to view its history and to create transactions that have to be signed with the offline wallet before being broadcast on the online one.
Create an offline wallet
Create a wallet on an offline machine, as per the usual process (file -> new) etc.
After creating the wallet, go to Wallet -> Information.
The Master Public Key of your wallet is the string shown in this popup window. Transfer that key to your online machine somehow.
Create a watching-only version of your wallet
On your online machine, open up Electrum and select File -> New/Restore. Enter a name for the wallet and select "Standard wallet".
Select "Use public or private keys"
Paste your master public key in the box.
Click Next to complete the creation of your wallet. When you're done, you should see a popup informing you that you are opening a watching-only wallet.
Then you should see the transaction history of your cold wallet.
Create an unsigned transaction
Go to the "send" tab on your online watching-only wallet, input the transaction data and press "Preview". A window pops up:
Press "save" and save the transaction file somewhere on your computer. Close the window and transfer the transaction file to your offline machine (e.g. with a usb stick).
Get your transaction signed
On your offline wallet, select Tools -> Load transaction -> From file in the menu and select the transaction file created in the previous step.
Press "sign". Once the transaction is signed, the Transaction ID appears in its designated field.
Press save, store the file somewhere on your computer, and transfer it back to your online machine.
Broadcast your transaction
On your online machine, select Tools -> Load transaction -> From File from the menu. Select the signed transaction file. In the window that opens up, press "broadcast". The transaction will be broadcasted over the Bitcoin network.