And away we roll
In order to reroll 120 onto a 620 spool, you're going to need some 620 spools. If you're lucky, like I was, they were in the camera, otherwise, you're going to have to scour second-hand stores, thrift shops, antique stores, and garage sales. You can sometimes find them on the eBay as well, if you look hard enough.

Now that you have the 620 spindles and the 120 film, you're going to need a completely dark area to unroll, then reroll the film. You could sit in the bathroom, closet, basement or whatever, waiting twenty minutes or so until your eyes adjust and check for any light leaks, then plug the leaks and wait again, or you can use a nifty little trick my father taught me.

Take a heavy coat, preferably a long winter coat with a hood, zip/snap/button it up and fold the bottom of the coat about a third of the way towards the top. Next fold the hood down over the neck opening.

If the coat doesn't have a hood, you'll have to fold the top of the coat toward the bottom to seal the neck opening.

Now place the folded coat on your lap with the front of the coat facing down, like in Figure C. You now have a light tight bag that you can use to reroll the film merely by inserting your hands through the sleeves of the coat.

FIGURE C

A properly folded coat makes a light-tight bag. Click picture for a larger image.

Since you're going to be rolling this film by feel, you may want to do a few dry runs in the light with a sacrificed roll.

Let's look at the 620 spools. You'll notice in Figure D there's one wide slot and one not-so-wide slot. When you roll the film onto this spindle, you want to feed it into the wide slot and out of the smaller slot. Remember, this will have to be done by feel.

FIGURE D

Notice the 620 spindle has one wide slot and one narrow slot. Click picture for a larger image.