Here are the mechanics of the NGFF SSD removal and installation

NGFF stands for "Next Generation Form Factor".  SSD is of course, "Solid State Drive".  These drives are 22x42x1mm (aka "2242").  There are also NGFF SSDs that are much longer (2260,2280...) and those will not fit in the Chromebook.  On the left is one I installed, on the right is the original HP part.

Note:  I had problems with this 128GB drive.  

ChromeOS somehow was corrupting the GPT and would not boot.  I tried Chrome recovery and now this drive will not boot at all.  I am trying to figure out how I can repair it. I think I will get an adapter so that I can connect it via USB and re-write the partition tables. I re-installed the OEM 16GB SSD and everything is working again using ChromeOS and Crouton/Saucy Salamander.

Here are the step-by-step instructions:

1. Things you will need:
• HP Chromebook 14 (Late 2013 model; ChromeOS version is "Falco")
• NGFF SSD
• #0 and #1 Phillips screwdrivers
• Plastic prying tool (I sharpened the end of a plastic fork with a file)
• You should wear a grounded Anti-static wrist strap
• I recommend you take photographs as you go along for reference when you get to the re-assembly stage
2. Backup any important files stored locally on your Chromebook.
3. Create a ChromeOS Recovery on a USB memory stick.   Remember, your version is "Falco".
4. Power-off Chromebook, disconnect external power, disconnect all peripherals, remove SIM card. Close the lid, turn it over and remove the 13 screws on the bottom.
   
   I've circled the 13 screw locations. Four of the screws are covered with small pieces of silicon rubber. You can pry them loose with a small knife. They have adhesive on them that can be re-used to attach them when you re-install the screws.
5. Turn the unit back over and open the screen.  Power-off the machine using the software-power-off button which appears when you click in the lower right-hand corner of the screen.  Gently pry the keyboard from the edge of the case using a plastic tool.  Start on either side of the trackpad and work your way around to the rear of the case.  The most difficult area will be below the center of the screen.
   
6. Hold the keyboard at an angle above the base of the unit.  First, disconnect the battery.  Next, disconnect the two ribbon cables for the keyboard and trackpad.  
   
   Here are the locations of the Battery, Keyboard, Trackpad and USB Ribbon cable connectors. You will be disconnecting these in that exact order.
   
   The flat, ribbon-like cables are removed by first flipping-up a small plastic latch.  Then pull the cable straight out of the connector.
7. Place the Keyboard aside.  Next, disconnect the Motherboard to USB Ribbon cable, Speaker cable, Cooling Fan cable and Wifi Antenna cables.  Connector locations are shown below.
   
8. Remove the 3 screws that hold down the battery and remove it.  While lifting the battery, shift it slightly to the left because the SIM Card PCB overlaps the right edge of the battery.
9. Remove the screw that holds down the Wifi mini-PCI card and remove it.
   
10. Remove the 3 screws that hold the Cooling Fan in place and remove it.
    
11. Remove screw and loosen PCB board adjacent to right-hand side of the screen's hinge.
12. Remove 3 screws, lift and slide Motherboard to the right.
    
    To access underside of Motherboard by lifting the lower edge up towards the Chromebook's screen. You may wish to cover the screen to prevent possible scratching.
    
13. Remove the screw that holds down the NGFF SSD and remove it by pulling it straight up.
14. Install the replacement NGFF SSD. It will only fit one way with minimal force.
15. Reassembly is to follow the steps in reverse. You will need to make sure you angle the Motherboard down and to your left to make sure you get the external connectors inserted through the case openings.
    
16. Before you close up the case, make sure you have connected all of the cables correctly and that they are routed to avoid any possible stress. When you close the case, apply pressure as shown.
    
17. When the Chromebook powers up (as soon as you connect the battery) you will see this screen. Insert your ChromeOS recovery USB memory stick.
    
18. Following, are the remaining screens that will walk you through the recovery process (should take about 5 minutes).
    
    
    
    
    
    
    
19. Remove your USB memory stick and the system will reboot. Connect to a network, log-in and type "chrome://quota-internals" into the search bar.
    
20. Now you can see your new storage capacity.