Queue class with enqueue and dequeue
Your code is correct as far as I can see. However, there are some
things which can be improved or simplified.

Let's start with the class Node definition:


Strictly speaking, data and prev are properties.
prev is – as I understand it – a pointer to the node that was added after this one, so I would call it next instead. 
The class should be private because it is not indented to be 
used outside of Queue.
data should be a constant because it is not mutated after the
creation of a node (attributions go to @Feldur who noticed that in
a comment).
Minor note: There should be a space before curly braces.


Then we have:

private class Node {
    // properties
    let data: String
    var next: Node?

    init(data: String) {
        self.data = data
    }
}


Consequently, head and tail are private properties as well:

// properties
private var head: Node?
private var tail: Node?


The enqueue() method can be simplified. head and tail are both
nil or not, so there is no need to check both. Here it makes sense
to check the tail via optional binding, so that a new node can be
appended if the list was non-empty, or a single-node list created
otherwise:

func enqueue(e: String) {
    let node = Node(data: e)
    if let lastNode = tail {
        lastNode.next = node
    } else {
        head = node
    }
    tail = node
}


The dequeue() method returns the string "empty" if the queue is 
empty. This is a "magic string" and makes it impossible to store the
string "empty" itself in the queue. Swift optionals were make
for this very purpose: The method should return an optional String?
which is nil if the queue is empty.

The method can be simplified in a similar manner as enqueue().
Now we check the initial node via optional binding. Note that there
is no forced unwrapping (!)  anymore, which should generally be
avoided:

func dequeue() -&gt; String? {
    if let firstNode = head {
        head = firstNode.next
        if head == nil {
            tail = nil
        }
        return firstNode.data
    } else {
        return nil
    }
}


In your test code, the queue variable can be defined and initialized in
a single statement:

var q = Queue()


Since dequeue() now returns an optional, we can remove elements in
a loop like this: 

q.enqueue("One")
q.enqueue("Two")
q.enqueue("Three")

while let s = q.dequeue() {
    print(s)
}


Finally: There is nothing in the implementation which is particular
to strings. You can make the class generic so that it can be used
with other data types as well. Only minor modifications are 
necessary:


Replace Node by Node&lt;T&gt; (and move it outside of Queue, as 
Swift currently does not allow nested types in generic classes).
Replace Queue by Queue&lt;T&gt;.
Replace String by T.


Then it looks like this:

private class Node&lt;T&gt; {
    let data: T
    var next: Node?

    init(data: T) {
        self.data = data
    }
}

class Queue&lt;T&gt; {

    private var head: Node&lt;T&gt;?
    private var tail: Node&lt;T&gt;?

    func enqueue(e: T) {
        let node = Node(data: e)
        if let lastNode = tail {
            lastNode.next = node
        } else {
            head = node
        }
        tail = node
    }

    func dequeue() -&gt; T? {
        if let firstNode = head {
            head = firstNode.next
            if head == nil {
                tail = nil
            }
            return firstNode.data
        } else {
            return nil
        }
    }
}


Test code:

var q = Queue&lt;Int&gt;()

q.enqueue(1)
q.enqueue(2)
q.enqueue(3)

while let i = q.dequeue() {
    print(i)
}