On European intervention in US Civil War.
The most likely to intervene were of course Britain and France. Both (especially Britain) had a need for southern cotton, though Britain was able to develop other sources during the war in Egypt and India. One problem for the South was that prior to the war there had been huge surpluses of cotton production--at the very time when European intervention was most likely (early war) the European warehouses were still stuffed full with old cotton. Only during later war did supplies begin to be affected, but by then it was too late. Next point is that both Britain and France wished to see a balance of power situation in the Western hemisphere--the independent South could help to balance the North and to help restrain its aggressive, expansionist tendencies. France also wanted to set up Mexico as its own puppet colony, and this venture received support of the South. This puppet Mexico could only continue to exist after the war if the South had won--a Northern victory would mean an aggressive US dismantling of the puppet regime in Mexico (which is exactly what happened historically). Plus, having the South independent would weaken the North in its commercial competition with Europe, also to the advantage of Britain and France. Finally, they wanted to rub the face of the US into the mud over the arrogant "Monroe Doctrine" in which the weakling US had granted itself exclusive control of the Western hemisphere against all Europeans--ironically the only reason that the Monroe Doctrine had seemed to work was because Britain chose for its own purposes to enforce the ban on European infiltration with its own naval forces--thus, the Monroe Doctrine of the US was enforce by the British Royal Navy. Anyway, it would have been fun to humiliate those cocky Americans by permanently splitting their country.
All of this just shows that Britain and France wanted the South to win. The key thing, though, is that they did not want to become involved too much in the war unless it became clear that the South could "win". Nonintervention was for them wiser than intervention on the losing side. A Southern victory does not mean full occupation of the North but exhaustion of the North until it accepted peace with the South--a Vietnam-type victory, if you will. However, although the South came close to "beating" the North (that is, hurting it enough to make it stop trying to reunify the country) in the early stages of the war, they never came quite close enough. Antietam is often listed as the great turning point in the diplomatic-military calculations. Anyway, so it was a big "Catch-22": South could only win a decisive military victory with European support, but that support would only be forthcoming after such a decisive military victory.
France (Napoleon 3) often wanted to intervene, but chose always to place itself at the service and disposal of Britain ("we will intervene, but only if Britain chooses to do so."). Thus, Britain became the key decision-maker in terms of intervention. But they never quite overcame their hesitations--nobody wants to bet on a horse unless it is going to be the winner.
Intervention could have taken many ways. There was simple recognition of the South, which Northern threats and bluster seem to have prevented. Another possibility is the offer to mediate--if rejected by the North, then this would have probably been followed by full declaration of war. Key aspects of interventionist power would have probably been naval. Commitment of British and French naval power would have broken the Northern blockade and allowed the South to get needed arms and supplies. Europeans had learned the secrets of the ironclad not from the US Civil War (as American textbooks often argue--"look at how the whole world learns from glorious America!" BS.) but from the Crimean War. They would have loved to crush North in naval battles. But again, the risks were just too great. Intervention by land troops could have been possible, for example, British troops from Canada, but mostly the naval aspect would be the decisive military contribution from Europe had intervention occurred.
Side note: the great power supporting the North the very most was Tsarist Russia. In return for this support, the US allowed the Russian naval forces to seek refuge in San Francisco and New York when war threatened later between Russia and Europe concerning crises in Eastern Europe, Poland, etc. Ironic, because it would have been a lot better for Russia later if the US had been split up into two parts and thus weakened. In the end, the North's ability to unify their country allowed them to expand aggressively and militaristically to conquer much of the world. How stupid Gorbachev is to have done exactly the opposite, by the way! Instead of keeping our country unified and marching to greatness, that dirty bastard divided us (temporarily) into little pieces. Our current defeats arise precisely from this division. Unity brings strength, and strength brings victory. The North knew this very well, so let's have a toast to the American North.