Swift is not distributed through the default Ubuntu package manager. This means that you cannot install with apt-get install . What you need to do is download the compiled Swift package from swift.org . Run wget first to get the Swift package in a compressed .tar.gz file.
$ wget https://swift.org/builds/swift-2.2-release/ubuntu1510/swift-2.2-RELEASE/swift-2.2-RELEASE-ubuntu15.10.tar.gz
Then you need to unzip the file by running
$ tar xzf swift-2.2-RELEASE-ubuntu15.10.tar.gz
This will unzip the file and create folders where the binary files are located. Go to swift-2.2-RELEASE-ubuntu15.10/usr/bin/ and make sure swift exists. You can start it by entering it in the terminal window.
$ ./swift
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