I have read quite a few posts on this, but I am still unsure about the correct approach, assuming:
  1. I have a default Ubuntu 14.04 LTS VM created by and running on Azure, which doesn't come with a swap
  2. I would like to create a swap using existing VM storage, instead of create a new disk using additional storage
I was also in need for this (actually 16.04 instead of 14.04, but my answer will apply to both I think).
Posts I have read:
But when I saw I had to read so long essays that you point out, I was going to give up... But suddenly I remembered a very straightforward article in DigitalOcean's blog:
How To Add Swap On Ubuntu 14.04
It's so simple that I've even written a script for it (at least for the best part, not yet the swappiness settings and other advanced stuff):
#!/usr/bin/env fsharpi
open System
open System.IO
open System.Net
open System.Diagnostics
#load "InfraTools.fs"
open Gatecoin.Infrastructure
// automation of https://www.digitalocean.com/community/tutorials/how-to-add-swap-on-ubuntu-14-04
let NUMBER_OF_GB_FOR_SWAP = 1
let isThereSwapMemoryInTheSystem (): bool =
    let _,output,_ = Tools.SafeHiddenExec("swapon", "-s")
    (output.Trim().Length > 0)
if (isThereSwapMemoryInTheSystem()) then
    Console.WriteLine("Swap already setup")
    Environment.Exit(0)
let swapFile = new FileInfo(Path.Combine("/", "swapfile"))
if not (swapFile.Exists) then
    Tools.BailIfNotSudoer("Need to use 'fallocate' to create swap file")
    Console.WriteLine("Creating swap file...")
    Tools.SafeExec("fallocate", String.Format("-l {0}G {1}", NUMBER_OF_GB_FOR_SWAP, swapFile.FullName), true)
let permissionsForSwapFile = 600
if not (Tools.OctalPermissions(swapFile) = permissionsForSwapFile) then
    Tools.BailIfNotSudoer("Need to adjust permissions of the swap file")
    Tools.SafeExec("chmod", String.Format("{0} {1}", permissionsForSwapFile, swapFile.FullName), true)
Tools.BailIfNotSudoer("Enable swap memory")
Tools.SafeExec("mkswap", swapFile.FullName, true)
Tools.SafeExec("swapon", swapFile.FullName, true)
if not (isThereSwapMemoryInTheSystem()) then
    Console.WriteLine("Something went wrong while enabling the swap file")
    Environment.Exit(1)
Tools.BailIfNotSudoer("Writing into /etc/fstab")
Tools.SafeHiddenExecBashCommand(String.Format("echo \"{0}   none    swap    sw    0   0\" >> /etc/fstab", swapFile.FullName))
For the above to work, you need to sudo apt install fsharp first (at least Ubuntu 16.04 has fsharp in the repositories, not sure about 14.04).
Also you need this InfraTools.fs file:
open System
open System.IO
open System.Net
namespace Gatecoin.Infrastructure
module Tools =
    let HiddenExec (command: string, arguments: string) =
        let startInfo = new System.Diagnostics.ProcessStartInfo(command)
        startInfo.Arguments <- arguments
        startInfo.UseShellExecute <- false
        // equivalent to `>/dev/null 2>&1` in unix
        startInfo.RedirectStandardError <- true
        startInfo.RedirectStandardOutput <- true
        use proc = System.Diagnostics.Process.Start(startInfo)
        proc.WaitForExit()
        (proc.ExitCode,proc.StandardOutput.ReadToEnd(),proc.StandardError.ReadToEnd())
    let HiddenExecBashCommand (commandWithArguments: string) =
        let args = String.Format("-c \"{0}\"", commandWithArguments.Replace("\"", "\\\""))
        HiddenExec("bash", args)
    let SafeHiddenExecBashCommand (commandWithArguments: string) =
        let exitCode,stdOut,stdErr = HiddenExecBashCommand commandWithArguments
        if not (exitCode = 0) then
            Console.Error.WriteLine(stdErr)
            Console.Error.WriteLine()
            Console.Error.WriteLine("Bash command '{0}' failed with exit code {1}.", commandWithArguments, exitCode.ToString())
            Environment.Exit(1)
        exitCode,stdOut,stdErr
    let Exec (command: string, arguments: string, echo: bool) =
        let psi = new System.Diagnostics.ProcessStartInfo(command)
        psi.Arguments <- arguments
        psi.UseShellExecute <- false
        if (echo) then
            Console.WriteLine("{0} {1}", command, arguments)
        let p = System.Diagnostics.Process.Start(psi)
        p.WaitForExit()
        p.ExitCode
    let ExecBashCommand (commandWithArguments: string, echo: bool) =
        let args = String.Format("-c \"{0}\"", commandWithArguments.Replace("\"", "\\\""))
        if (echo) then
            Console.WriteLine(commandWithArguments)
        Exec("bash", args, false)
    let SafeHiddenExec (command: string, arguments: string) =
        let exitCode,stdOut,stdErr = HiddenExec(command, arguments)
        if not (exitCode = 0) then
            Console.Error.WriteLine(stdErr)
            Console.Error.WriteLine()
            Console.Error.WriteLine("Command '{0}' failed with exit code {1}. Arguments supplied: '{2}'", command, exitCode.ToString(), arguments)
            Environment.Exit(1)
        exitCode,stdOut,stdErr
    let SafeExec (command: string, arguments: string, echo: bool) =
        let exitCode = Exec(command, arguments, echo)
        if not (exitCode = 0) then
            Console.Error.WriteLine("Command '{0}' failed with exit code {1}. Arguments supplied: '{2}'", command, exitCode.ToString(), arguments)
            Environment.Exit(1)
            failwith "unreached"
        ()
    let SafeExecBashCommand (commandWithArguments: string, echo: bool) =
        let args = String.Format("-c \"{0}\"", commandWithArguments.Replace("\"", "\\\""))
        if (echo) then
            Console.WriteLine(commandWithArguments)
        SafeExec("bash", args, false)
    let FirstElementOf3Tuple (a, _, _) = a
    let SecondElementOf3Tuple (_, b, _) = b
    let SimpleStringSplit (str: string, separator: string): string list =
        List.ofSeq(str.Split([|separator|], StringSplitOptions.RemoveEmptyEntries))
    let SplitStringInLines (str: string): string list =
        SimpleStringSplit(str,Environment.NewLine)
    let CommandWorksInShell (command: string): bool =
        let exitCode =
            try
                Some(FirstElementOf3Tuple(HiddenExec(command,String.Empty))
            with
                | :? System.ComponentModel.Win32Exception -> (); None
        if exitCode.IsNone then
            false
        else
            true
    let BailIfNotSudoer(reason: string): unit =   
        if not (CommandWorksInShell "id") then
            Console.WriteLine ("'id' unix command is needed for this script to work")
            Environment.Exit(2)
            ()
        let _,idOutput,_ = HiddenExec("id","-u")
        if not (idOutput.Trim() = "0") then
            Console.Error.WriteLine ("Error: needs sudo privilege. Reason: {0}", reason)
            Environment.Exit(3)
            ()
        ()
    let OctalPermissions (file: FileInfo): int =
        let output = SecondElementOf3Tuple(SafeHiddenExec("stat", String.Format("-c \"%a\" {0}", file.FullName)))
        Int32.Parse(output.Trim())
Many solutions were discussed but I can't seem to find one that will persists across server reboots 
The part that makes my answer work through server reboots is the writing to /etc/fstab file.
The good thing about this solution is that it should work in Azure, DigitalOcean, YouNameIt, ...
Enjoy!