Most important: Be prepared!
On organized skating tours (at least in sweden) the following is mandatory equipment.
- An ice probe (to determine ice thickness so you wont go through in the first place)
- A backpack with a complete change of clothes in a watertight bag. The backpack must have a harness that goes between your legs so it doubles as a flotation device and can be used to pull you out of the water.
- Ice claws/spikes/"Isdubbar" (If you do go through, you stab them into the ice for traction)
- A rescue line. A line with a floating weight and a fixed loop in each end. Must be easily accessible even in water.
This is equipment that both the person in the water and people around are likely to have, even far from populated areas.
Once someone is in the water however, there are several means of rescue.
Rescue helicopter. Lets you get to the person in the water without putting the rescuer at risk. Lets you transport a hypothermic or injured victim safely.
This naturally is overkill in most cases.
A surf board or similar, that can be pushed out onto thin ice by spreading the load, and what floats if the ice breaks. The victim can grab the board and get up/be pulled up, or a rescuer can lay flat on it grabbing the victim while a second rescuer pushes/pulls the board from behind.
There are custom built boards designed for this. Naturally a plank, a ladder or a branch will do in an emergency. Anything that spreads the load, ideally floats and/or puts some distance between rescuer and victim.
A small boat works too, but might be harder to reach up to from the water.
Note: I put this as "second best", but only if such items are at hand. If you have a rescue line ant the victim is uninjured, don't waste time looking for a plank.
A line with a floating weight and a bowline (fixed loop) on both ends. Throw it to the victim. (Or even better, if the victim has one he/she can throw it to a rescuer)
Either put the bowline around your wrist or (if you came prepared) attach it to a carabiner on your backpacks harness.
Self rescue. Never go on natural ice unprepared! Wear something that will help you float. (Dry suit, life jacket or a water tight backpack) Bring a pair of "isdubbar" (Swedish. Don't know an english term) or simply two large nails. Stab them into the ice to get traction enough to get back up.
In any case, make sure that no one else falls through. Always try to get up in the direction from wich you came. And don't go out on natural ice unprepared.