As a general rule, heavy steel hands are easier to repair, since they are thicker and sturdier than very thin (more mass-produced) examples. Both types of hands, however, can be repaired in the same manner.
Repairing hands is relatively straight forward: Mend the break with a supporting piece on the reverse. Actually executing the repairs, however, can get very tricky.
In the case of the hands on this particular clock, we have two repairs to make (one on each hand). The hour hand was broken in half at some point, and simply repaired with an overlapped solder repair. The minute hand is missing about 3/4" from the tip.
As received:
To start, you will need to find suitable "patch" material. Ideally, you want thin steel with a good carbon content (such as spring steel, which isn't very flexible). Any usable scrap steel can be used. Thin saw blades, taper pins (which would need to be filed flat on two surfaces), or strong sheet metal. Keep in mind that the patch steel will now be taking the job of transferring the force applied to the hand, so you want a stiff metal. Try to stick to something relatively thin. A hacksaw blade could work, but it's getting a bit on the thick side. For this hand, I used a piece of relatively thick spring steel (scrap metal).
Coarsely cut or grind your patch to the correct width. You will want to cut it long enough to hold a good solder bond on each side of the break.
In this photo, you can see the patch piece, and the hand, which has been taken apart, and had the excess solder scraped away.
File, or otherwise abrade and clean the 3 surfaces to be joined (one surface of your patch, and a portion on each side of the hand - on the back).
Tin all 3 surfaces separately, and THINLY. For this type of repair, I'm using regular solder (mine happens to be silver bearing low-temp solder: 98% tin, 2% silver).
To make soldering all 3 pieces easier, I tie all the pieces tightly together using old window screen wire (visible in the photo above). This works well because the screen is aluminum. Aluminum will not stick to solder.
I also use one of those "helping hand" tools to hold the hand while it's heated.
As I mentioned earlier, these hand repairs can be tricky, and parts can move easily. Here was my first attempt:
If this happens, just desolder, re-flux, and redo the repair.
Once your pieces are properly aligned, sturdy, and cooled, you can start filing the repair. Start by squaring the edges. Once that's done, you will also want to taper all the other edges on the back in a pyramid shaped fashion. This can be done entirely by hand with files, or you can cheat and combine hand filing with the use of a grinding wheel on a Dremel tool (which is what I did).
Aim for something like this:
The purpose of tapering the repair is simply to make it look less visible from a slight angle when you're viewing the hand(s) from the front.
The front on this particular hand is not 100% perfect (especially if you're looking at an extreme close-up), but the repair came out quite well.
To finish the repair, you will need to use a cold method to colour the repair and solder, such as Gun Blue, or paint.
Here is the completed hour hand:
I didn't photograph any of the repairs to the minute hand, but I'll explain what I did.
For the minute hand, I decided to cheat and make both a beautiful, solid, and easy repair. Since the hand terminates in a very gradual point, I simply chose an appropriately shaped steel taper pin for the repair. I did not need a 3-piece repair here. I simply filed a notch into the end of the pin until the hand fit into it flush on the top surface. Once soldered, the front and back of the pin were filed down, and the repair is nearly invisible.
Back:
I have used the same techniques described above to repair other hands with equally good results.
