The Slippery Slope argument is generally that we should not do one thing because it will lead to another thing, and then another, and then another, until you go crashing into the bottom. It is a way to make an opponents argument seem more extreme by saying if you do one thing (action A), it will lead to something else (action B), which will eventually lead to an extreme (action Z) which EVERYONE knows is wrong and doesn't want. The inference being that to avoid that really wrong thing, we must avoid doing anything (or at least action A).
A common example might be, "if you have cigarette or drink of alcohol, this will lead to experimenting with soft drugs (like trying pot), which will lead to heavier drugs (like Cocaine or Heroine) which will lead to lead to addiction, poverty and loss of job, family, motivation and possibly overdose and death". So the point is "do not to try cigarettes or alcohol or you will become a drug addict and die!".
The trouble is that slippery slope is a logical fallacy. Action A does not always lead to action Z. There are many stages in between, and many possibilities.
Using the example above, I know many people that have tried one cigarettes or alcohol who did not go on to other stages. One action did not lead to the other. I also know some people that jumped stages and went to light or heavy drugs without every starting on the more basic stages. So action A does not always lead to action Z. And some people get to action Z (or B, C, D, etc.) without ever going through A or in between stages (but this is a different point altogether).
So the whole premise of slippery slope arguments is wrong (action A does not have to lead to action Z).... and in a black and white world, it isn't white (logically true) so it must be black (logically false). Sadly, our world isn't so clearly polar and easy to decide.
Despite being logically wrong, slippery slope can still be historically or statistically correct. So Slippery Slope arguments are sometimes right and are still valid in debate/discussion to talk about POTENTIAL consequences (or likely), as long as you aren't arguing that they are absolute consequences. So while action A does not HAVE to lead to action Z, the question is how likely is it to do so?
If 25% of people who start smoking become addicted to nicotine (and become heavy smokers, and suffer the consequences in cost, health and so on), then it is completely valid to point out that you shouldn't start smoking because of the risk to become a heavy (addicted) smoker. It is a slippery slope argument to claim you shouldn't start smoking because of what it can lead to -- but it is also a valid argument that should be discussed. And 25% is still a relatively low probability -- there are other examples where it might be 80%, 90% or even more likely to happen. Potential consequences matter, likelihood is a valid concern.
There are many cases where something doesn't HAVE to another -- but always (usually) does. Again, the slippery slope argument is still logically wrong -- and again, the point you are making may still be correct despite the logical error of the argument itself.
Communism doesn't have to become a totalitarian regime that disregards human rights. Marx's theoretical workers paradise is a potential theory and could exist. Yet the facts are that in order to create the parity of income required to achieve the "people's paradise" (and take from the have's to give to the have not's) you must give government (and a few leaders) extraordinary powers, and you must overthrow the current leadership and infrastructure. Once the revolution is done, the power is very focused (by an elite few), and the power is very easy to abuse -- all in a nation that is unstable (communism is not the ordinary state of humanity, so things are "wobbly" at best). In order to stabilize the Government the leaders will usually eliminate the competition and use their power to do things to stabilize themselves in their positions of power, and of course to micromanage the economy (and keep everyone "equal") -- and the end results have always been a less free, more repressive society.
Action A does not HAVE to lead to Action Z -- it just does! So it is logically incorrect to assume action A has to lead to action Z -- but it is often historically accurate and likely. Causes have effects (and vise versa), and if it has always happened before, it is likely to happen again.
Often using a slippery slope argument (or explaining it and drawing attention to it) is to explain that the first action is wrong. It is not just wrong because of where it is likely to (or may) lead -- it can be wrong in and of itself. People often explain this by extremes (taking the little wrong and showing it in a more dramatic way -- by following it down the path/slope). The whole path is wrong, and you are really using extreme examples of where it is likely to go to show that.
I use these examples in many different cases. Like some people I know have attacked smoking as a "risky" behavior (health wise), so I point out that sex, diet, genetics, stress, exercise and other behaviors effect people's health far more than smoking -- and that if they want to legislate other people's vices, then the others will come back and legislate theirs (and they are setting precedence and giving ammo to the opposition). So I say, "If you legislate smoking, then they will legislate McDonalds, our bedrooms, try to bring back eugenics, and so on". They cry foul and charge, "slippery slope = logical fallacy". Well, it is a slippery slope argument, so they are correct to point that out, but it is more than just a slippery slope argument. It is also somewhat historically proven that if you give people a new power (or rationalization) that they will actually use it. My example is also explaining how their action is wrong on its own, using the old "how would you like it if..." or basically my way of explaining "tit for tat". If you assume (create) that power for your cause (new use of law), then others will use that same power for their cause. So the point is that not only is slipping to some extreme ends likely and wrong, the means itself is questionable, and is demonstrated by applying it to other things. It doesn't have to happen, but likely will. Not only is further down the slope wrong, but right where you are is wrong as well -- and is noticeable if you apply the same powers to others. The means to an end can be slippery and wrong, without ever sliding to the extreme conclusion.
It is a very tricky balancing act on when to use and not use slippery slope arguments. We can't be paralyzed into doing nothing as a society (or individuals) because of some rare consequences -- and we shouldn't pretend that anything we do will lead us plunging into the depths of chaos. So we should question slippery slope and what is likely. But we also shouldn't pretend that there are no consequences to our actions, or speculate about cause and effect either. We need to think about consequences, and that requires looking at the lay of the land (and the angle of the slope). Again, slippery slopes exists, and are we willing to accept the slippage -- and is this the right path to be traveling down at all?
It gets very hard to know when an argument is only a slippery slope fallacy, and when it is a slippery slope example that has a lot of validity. I know that any time a slippery slope argument is used it should set off warning bells. But just because a slippery slope is logical fallacy, does not mean that the argument or points made by the argument are wrong. Arguments made by "slippery slope" are not proofs -- but to assume that they can't happen (or are not likely) is a logical fallacy as well. They can happen, they do happen, and they might even be historically or statistical inevitability's. Just be ready to argue those points and not think that using a slippery slope either proves anything on its own, or that the use of that type of argument disproves anything.