This is how I disassemble a CV joint (sometimes known as a brunfield) 

Tools needed:

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Safety glasses

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Rubber mallet

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Bench vice

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Small screwdriver 

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Degreaser/Varsol cleaner (Brake cleaner) 

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Shop rags

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WD-40

Time to do disassemble and reassemble both sides about 1 hour

                       

sepration of the CV shaft Put safety glasses on then clamp inner shaft in a vice.

Do not clamp on seal surface and splines.

Using one hand and grasping the outer CV shaft then use a large rubber mallet and tap on the CV.

Removed CV axle It should pop right off.

If not tap harder. The resistance is from the "C" clip on the other end. The objective is to uses enough force to collapse the "C" clip into the grove.

Inner axle shaft showing C clip and spacer Here is the "C" clip along with the spacer.
removal of the C clip

Using a small screwdriver carefully pry & lift the "C" clip off the shaft.

It is sometimes good to have a rag laying over the shaft at this point to keep the "C" clip from flying across the garage. Afterwards slide off the collar and clean and inspect for cracks or imperfection on the splines.
(Make sure you have safety glasses on)

CV stub axle clamped in a vice Clamp the outer stub shaft in a vice.

Do not clamp on the splines and/or the seal surface.

A rag can be used to prevent marring of the shaft but it will not clamp as well.

mvc-024f.jpg (48228 bytes) Mark the stub axle and inner piece with a marker for reference and orientation during reassembly. 
mvc-025f.jpg (48893 bytes) Using your finger rotate the inner to let one of the ball bearings come upward.
mvc-026f.jpg (56576 bytes) Remove the ball bearing and set aside in a secure location. 
mvc-027f.jpg (49129 bytes) Rotate around with your finger and continue to the next ball bearing.
Mvc-028f.jpg (49212 bytes) There will be a point where the inside cage will rotate around easily and the rest of the bearings can be removed.
mvc-029f.jpg (47668 bytes) Rotate the cage around and position the inside like so.

Lift upward on the inside star piece and rotate and lift outwards.

mvc-030f.jpg (52281 bytes) When positioned correctly, it will come right out with no effort and prying. 
mvc-031f.jpg (48994 bytes) Rotate the cage around to this position and it to should come out with no resistance.
Mvc-032f.jpg (50817 bytes) After removing inspect the inside of the stub axle carefully.

Run your fingers inside the ball friction area to feel for burs or high spots.

The stub axle is flame hardened so discoloration around the edges and inside is normal because of the hardening process.

mvc-033f.jpg (58565 bytes)  Clean all parts and inspect for chipped bearings and cracked cages. Pay attention not to wipe off the orientation mark that was colored on previous.
mvc-034f.jpg (48313 bytes) Reassemble by reverse procedure.

Install the cage with no force, it should drop in if positioned correctly.

mvc-035f.jpg (51385 bytes) make sure it rotates freely inside.

spray lightly with WD-40 if needed.

mvc-036f.jpg (50141 bytes) The inside star will go in the opening and will drop in with no force. you may have to wiggle the cage around to make it seat in.
Mvc-037f.jpg (48347 bytes) Making sure the orientation is correct and in the proper position, install a couple of ball bearings in the seat.
Mvc-038f.jpg (51244 bytes) The hardest part is the last ball bearing. It helps if you lightly pry upward on the inside star . Pry only far enough to insert the last ball in the cage.

(don't use any soft material like a brass punch to pry with because the metal filings will go inside the clean CV)

Mvc-040f.jpg (48918 bytes) After installing the collar & "C" clip on the end of the axle shaft, reinsert the inner axle shaft by pressing down hard and having the "C" clip collapse in the grove.

It will pop into place because the clip will spring open when it passes thru the end of the splines.

  Afterwards you can cut a tube of Swivel grease and fill around the CV then install in the front axle.

If just for storage & spare spray liberally with WD-40