The issues that omgrybread mentioned are issues that show different parties wanting to use government control in different aspects of a citizen's actions and shows that the parties aren't just more government versus less government.
Presumebly for an issue, left wing and right wing just comes from more government versus less government or guidance versus freedom.
However, for parties and voters, I still find it hard to understand how people can say things like 'The Nazis are right wing' when there are obviously a lot of issues involved. (and that's not even getting into whether the Nazis are really right wing.) Perhaps in this case, the definitions come from what the 'core' beliefs are? (I feel like I'm wrong here, so feel free to rip this statement apart)
Very very basically, right and left wing boils down to hierarchy.
"Right-wing politics" is an incredibly broad umbrella of political philosophies that support a hierarchically ordered society and rejects egalitarianism. "Left-wing" refers to, again, a broad range of philosophies that support equality and reject the supremacy of certain individuals.
Nazis (and other facists) are right-wing because they involve a strong dictator and state that are nominally and practically above the citizenry. Royalism, Theocracy, traditional conservatism, and Christian democrats all obviously fit in this group as well. Classical liberalism, neo-liberalism, anarcho-capitalism, minarchism, libertarianism, and the other "liberty" style philosophies fit into the right wing as well, because they end up with a de facto hierarchy. In the most extreme example, anarcho-capitalism, the capitalists are at the top of the ladder and unskilled laborers at the bottom.
The difference between the two major groups of right-wing politics is that the "conservative" types encode the hierarchy within law, and the "liberal" types have the hierarchy only exist in the market. It's theoretically possible for their elite to lose power without altering the political structure.
Left-wing politics includes left communism and anarcho-communism at it's far end, and social liberalism at the center-left. Left-Communism, Leninism*, Maoism, worker-owned capitalism, etc, all form the "anti-capitalist" type of the left-wing, in which egalitarianism is enforced by the elimination of traditional capitalism. The other major type is the welfare-state capitalism of Progressivism and modern liberalism.
There's a major difference in the two. Both "types" of right wing politics can exist anywhere on the spectrum. Christian Democrats and theocrats are similar in style, even though one is centrist and the other is far-right. Anarcho-capitalists are far-right, and classical liberals are centrist. On the left, though, communism and it's various types are far-left, and the capitalist welfare-state philosophies are more centrist, with few exceptions to each, and those can be kind of stretched or unfeasible.
*Leninism is starred above because it's very odd. At first glance Leninism appears to have many right wing elements, and it does. Without wasting 5 pages on it, Leninism was never intended as a truly communist system of governance. It was to be a placeholder until the dictatorship of the proletariat was not needed. Obviously it didn't work.
With these new, awesome definitions, almost every political philosophy is covered! Ask yourself if it supports egalitarianism or not, and boom, there's an answer. Almost every though, because there is an extremely tricky beast (well, one I can think of right now, I'm sure there's more hard to define philosophies.) Stalinism is nominally communist, yet in practice, it's perhaps most closely related to facism. Trotskyism and Left-Communism reject Stalinism as right-wing, in fact. It's extremely hard to define, and perhaps the best answer is that Stalinism is not a political philosophy at all, but merely a government style similar to the neopatrimonialism of modern Big Man dictatorships.
Phew. That was somewhat tiring. But yeah, that's pretty much the proper, universal answer to the OP's question. It's only related to normal usage of the terms in a somewhat abstract way, though.
EDIT: Maybe I'm tired, but rereading my post, it basically makes no sense. There's a point in there if you can decode the horrible writing, but I apologize for the messiness and absurd amount of -isms. It reads like the worst kind of non-fiction writing.