• Nylon carpet thread or wax linen.  About 6 to 10 m. for full restitch of top and bottom halves
• Two size 22 needlepoint or tapestry needles (they have blunt tips).
• Seam ripper
• A few small safety pins
• A pair of scissors-type tweezers
• Awl or large needle
• Mink oil conditioner

I recommend a liquid conditioner, rather than the cream or paste types, which are more of a surface treatment.  Using a liquid oil allows penetration deep into the leather. 

Removing the Old Stitching 
Once the leather has been conditioned you can begin to remove the old stitching.  You may find it helpful to "un-stitch" only half at a time, leaving the opposite side in place for comparison. (Some spots around the perimeter of the seams may require a special stitch) 
  
Carefully remove all the old stitching in the area you wish to repair.  Use care  to avoid damaging the holes.  Just yanking the thread out or pulling on opposite sides of the seam could easily damage the old leather.  It helps to cut every stitch along both side of the seam, using a seam ripper or similar tool. (Fig. 1)  Pull these segments out with tweezers, then carefully pluck out any remaining pieces. 

As you remove the old threads, put a small safety pin through a set of holes occasionally to keep the holes matched and the case partly assembled, then remove them as you stitch. (You only need two or three pins per side.) 

Re-stitching 
When the threads have been removed, go around the seam with an awl, twirling it into each hole, slightly enlarging and smoothing the sides.  This will make it easier to accomplish the re-stitching. 

Cut a 60" (1.5 m) length of thread.  Thread a needle an inch or two onto each end.   

You will be tying off the thread inside the case when you reach the halfway point, so you want to start at the front and work your way around.  

Start by running one needle through the first set of vacant holes.  Pull the thread halfway through,   like starting to lace a pair of shoes (Fig. 2) then run this needle back through the next set of holes.  Do not leapfrog or skip a set.  You want to go through each set of holes in turn. 

Pass the other needle back through this same hole, then pull snug.  (Fig. 3)  

Continue in this fashion, essentially forming a continuous figure 8 with the thread.  Every three holes or so, put an overhand knot in the two threads where they pass through.  This will keep them from loosening. (Fig. 4) 

Last Hole 
When you reach the last hole (generally at the midpoint) carefully work the needles into just the first piece of leather from each side but not into the second, pushing the needles through to the interior of the case. 

Note:  Some holes are more shallow than others and attempting to work the needle through these shallow holes and on into the case in one step may cause the hole to tear.  This can be avoided by running the needle completely through the hole to the outside, then running the needle back down between the two pieces of leather and into the case. (Figs. 5a and 5b) 

 Working from inside the case, pull the threads snug, then securely tie the two ends together.  Clip the excess thread and tuck the knot down out of the way.  (Fig. 6) 

Repeat for the opposite half, again ending in the center.