That's a tough question, PotR. I'll confess this from the start: You have to experience it to understand it clearly. While I had the knowledge and arguments down...the thing that most drove it home was the practice once I had accepted it. When I had done veneration, I began to see the difference. It's not easy to put into words, either.
Part of the answer applies to what the target is, frankly. Worship is ascribed to God, and if we worship anything but God, then this is idolatry. Worship involves the presentation of sacrifice, absolute adoration, ascription of traits belonging only to God, and so forth. So, when I venerate an icon, of say, St. Herman of Alaska, and pray to him (not to the icon), I am not worshipping him.
However, if I hold a religious service and present a sacrifice to him (maybe like that of the Eucharist, for instance), then I have crossed he line. The Eucharist represents Christ, and He alone. No sacrificial meal is permitted to anybody but Christ (God).
The next thing to remember is ancient paganism. The idol was a god. More specifically, it was a representation of the god that was like a little avatar. The idol acted as a sort of avatar. For this reason, when an idol was damaged, it was like the god was damaged, even though the god wasn't. It was with this understanding that one Father (I'd have to look up his name), explained that if the cross is broken, he may break it up and cast it into a furnace.
It is true that that oversimplifies things, because like the Old Testament, things are made holy, but it does explain a key difference, and it's one you can't simply wave away: the icon is completely separate from its subject. Only my intention, say of reverence or prayer may be transferred, and then, not because there is an icon, but because God allows the person in heaven to receive the veneration.
So, we have these attributes that I can name (off the top of my head) that separate icons from idols: the nature of veneration given the target, the nature of the target, and the identity of the target. For instance, worship given to a deity other than God is always idolatry.
The preceding is actually reflected in the Scripture. Pagan idols were condemned because they were deaf stone and wood. They could not act. They could not do anything, and they represented a god that the builder decided to fashion. However, they treated it as the god. They would serve it meals. They would sacrifice to it, and so on. The worship was given to the image, and it was even fed.
God, however, didn't make a blanket statement against images (using our Old Testament, since the situation is very complex). He commanded the construction of multiple images in the Temple. The highest sacrifice of the year was to be done on an image in the Holy of Holies. This same Ark of the Covenant was paraded around for war, preceded the people, etc. It was venerated, and on occasion those who did not treat it as holy were struck down. God also commanded the construction of a serpent. When the people were bitten by the vipers in the desert, they would look to a bronze image for healing, but this same image later became an idol and was destroyed. The veneration God assigned was acceptable, but the worship that came later was not.
This attitude about veneration/worship even applies to bowing. When someone bowed down to a man, authority figure (such as Pharoah), or the like, he was well within his God-given paramaters. However, John bowed before the angel in Revelation, the exact same action was forbidden. Why? The heart and the veneration involved. The former was mere veneration, while the latter became idolatry, because he ascribed to an angel the fear he owed God alone.
We, also, venerate people and images in everyday life, and we do not consider it idolatry (well, most of us). For instance, when I pledge to the flag, I am not worshipping it. I am venerating it. When a funeral procession goes by, I stop what I am doing out of reverance for the deceased. This is not worship. This is veneration. Likewise, if someone kisses a picture of their spouse and even talks to it, they aren't worshipping the picture or the person in the picture.
Perhaps the best modern example is the Bible. I reverance the Bible, and I take it as an authority on my life. It is, however, a book. It's a piece of paper with ink on it. If I tossed it into the fire, it would burn just as easily. However, I would wager most Christians on here treat their Bible with respect, and if someone spit on it, they would take it as malice towards God. The action and intent directed toward the Bible, thus, is directed toward God. However, the two cannot be equated in any way.
I'm afraid I cannot address idolatry in modern paganism. I have never been one, and I have no sources that I have really read. As such, I could do nothing with modern paganism but construct a scarecrow. I will not do that.