Super Glue is a cyanoacrylate. That is the sticky stuff in all of these types of glue. The best way to remove super glue is with Mister Glue’s Un-cure.  It is designed to safely remove super glue.  Below is a list of other glues containing the same base, cyanoacrylate, as super glue.

Mister Glue’s Uncure will work for these plus other
similar products:
Krazy Glue
Mister Glue
Max 1
Miracle Glue
Loctite
The Last Glue
Pasco Fix
and Rhino Glue and more.

Acetone can also be used for removing super glue. It is much more toxic so be careful  It be found as nail polish remover at your local pharmacy. Nail polish remover is usually composed of acetone. Some are ‘acetone free’ which is not very useful so check the bottle first.
Be cautious about what you put the acetone on when cleaning super glue. Acetone will eat away at paint usually and some plastics.

Other types of super glue removal:
Sometimes with these types of materials: plastics, paints, etc, it is easier to let the glue dry up a bit and gently scrape it off with an Exacto knife blade.

If you are worried about getting super glue on your skin, it wears off fairly quickly. Warm soapy water will usually help, though I would start with Mister Glue’s Un-cure.   Once cleaned up a bit pour some in the sink and let your fingers soak a few minutes. Mister Glue and other cyanoacrylates are not water soluble but will not stay stuck to the oils in the skin. If your skin is a bit drier super glue may stick a little harder and take a little longer to come off. If you are getting your hands to sweat a bit the oils will tend to lift off the glue.

Just about anyone that uses super glue or one of the different cyanoacylates will stick their fingers together at some point or another. Super glue, Mister Glue, Max One and these other glues can tear the skin if you are not careful. Have some Un-cure handy.  Even without this you should be able to gently pry your stuck fingers apart. You can gently peel them back. Do not try and just pull them directly away from each other. This is more difficult with dry skin.

Removing super glue from clothing or fabric is a little trickier. As acetone will damage many fabrics it is not the best thing to use. Mister Glue’s Un-cure can be used safely more often.  Test a small amount of Un-cure to make sure it is not going to damage the material.

Another trick as a super glue remover is to use ice – freeze it. It becomes brittle and then you can break it off. A piece of clothing can be put in the freezer. On furniture or a carpet try some ice cubes in a plastic sandwich bag. Hold it against the spot. Even once off the fabric may continue to remain stained.

The best thing with super glue is prevention. That is tricky to do with hands but as noted above it is not that difficult to get off. Use a piece of cardboard under the area where you are using the super glue or Mister Glue. Do not use fabric or thin paper as the glue can easily seep through and stick these materials to the table or whatever is underneath.

Other articles/pages that may interest you:
Super Glue in the Eye
Instructions for Use Of Mister Glue
Types of Glue