This is the simplest set of steps that I've found so far in order to get Swift on (Ubuntu) Linux. Essentially, you can download a snapshot and you're good to go.

If you're not already on Ubuntu 15.10, create a VM. Vagrant is an easy way to do this:

$ vagrant init ubuntu/wily64
$ vagrant up
$ vagrant ssh

Install the dependencies:

$ sudo apt-get install clang libicu-dev vim

(Vim isn't an actual dependency, but I can't cope with terminal that doesn't have it!)

Grab a Swift snapshot & untar:

$ cd ~
$ curl -O https://swift.org/builds/development/ubuntu1510/swift-DEVELOPMENT-SNAPSHOT-2016-04-12-a/swift-DEVELOPMENT-SNAPSHOT-2016-04-12-a-ubuntu15.10.tar.gz
$ mkdir swift
$ tar xzf swift-DEVELOPMENT-SNAPSHOT-2016-04-12-a-ubuntu15.10.tar.gz -C swift --strip-components 1

I've used the latest snapshot as of this writing: check the website for the latest one as it is updated regularly.

The binaries are now in ~/swift/usr/bin, so add that to your path and you're good to go:

$ echo 'export PATH=~/swift/usr/bin:$PATH' >>~/.profile
$ source ~/.profile

Prove it works:

$ swift --version
Swift version 3.0-dev (LLVM 752e1430fc, Clang 3987718dae, Swift 36739f7b57)
Target: x86_64-unknown-linux-gnu

Now, you just need to learn Swift!