Of all the above, the one most everyone agrees is the wrong way of cleaning copper coins is by using polishing agents. This is because polishing actually works by removing the topmost atomic layers of metal and working downwards from there. Ideally, you want your coin's metal to stay and the dirt to leave.
Dissolving: By this we usually mean soaking in olive oil in the lock-it-up-and-forget-it category of coin cleaning. However, dissolving can also mean the use of acids such as lemon juice or vinegar which are more properly used to clean silver coins. Other than this particular case, the use of acids is emphatically not recommended for the same reason as polishing. You are wearing away at the metal in the hopes of carrying off the dirt too. Bad, bad. An alternative to olive oil, though no quicker, is mineral oil. The main advantage of mineral over olive oil is that it doesn't stain the coin dark. It is, in fact, a great way of preserving a freshly cleaned coin from future corrosion. Just apply a very light coat and the oil acts as sealer and protectant.
Scrubbing: you can't get away from scrubbing your coin. You really have to go out of your way to clean a coin without giving it a good workover with a brush! Some use brass bristled brushes but this is a dangerous procedure because it's metal on metal. Keep in mind that even a diamond is worn to the nubbins by nothing other than soft vinyl plastic. Therefore brass tools of any sort should ideally work on the dirt and never against the bare coin. For these reasons a toothbrush with stiff bristles is preferable as a general-purpose tool.
Prying: When the shotgun approach of brushing is over with you're often left with dirt still in the nooks and crannies of your coin. Rather than continue to brush it's best to finish the coin with some nit-picking. An X-acto knife can cut through the toughest adhesions and, assuming great care is taken, can do wonders for the stubborn dirt still left on your coin. The problem, of course, is that it can just as easily scratch your coin. Brass pins allow more leeway for error but are somewhat less effective. You will need to decide how much risk to take at the expense of speed and convenience.
Shocking: electrolysis, as described above. The most effective way of cleaning (but potentially most disastrous to your coin).
Freezing/Heating: in theory, when you heat a metal such as a coin it expands and when you cool it it contracts. Because the metal is resilient and the minerals piggybacked to it aren't, the dirt becomes brittle then falls off the way a clay mask would crack on your skin when you flexed it. In practice, however, little flaking is noticeable even when a coin is heated well past the boiling point then shock-freezed straight on ice. The reason is that the amount of flexing involved in that temperature range is too small to do much. Because it's fairly passive it is worth a try where gentler methods have failed.
Lastly comes pulling. Pulling? Yep, by way of using adhesives you can literally yank the crud off a coin's surface. This is the least talked-about method of coin cleaning and I'm not sure why. It works wonders although it's quite tedious and time consuming. The easy way of doing this is to stick your dirty coin on packing tape then pulling it off. Notice all the dirt that just came off? Repeat the steps until the coin comes off clean. Unfortunately, packing tape doesn't "pack" the adhesive power to pull off the whole job. That's why Elmer's glue is preferable. You put a drop or two on the coin face, smear it to an even coat and let it dry. Then peel off. Repeat til glue comes off clean. While this method is much quicker than oil-and-forget, it is not as gentle. Coins which have glossy patinas covered under dirt are the least recommended for this process because the glue tends to turn the surface opaque. It is also aggravatingly labor-intensive.