After Napoleon's exile to Saint Helena and before the revolutions of 1848, Europe was dominated by a conservative, sometimes reactionary system centered around protecting the political stability and rights of the nobility which had been traumatized by revolutionary France and Napoleon's campaigns. Apart from Great Britain and France, all of the European powers were absolute monarchies, held together by the authority of the crown and sensitive to the perceived threat of nationalist and liberal uprisings. The center of this system was found in Vienna with the ardent defender of conservative monarchy Klemens von Metternich, who had personally suffered from the tumultuous period after 1789 and felt that a monarchy that answered to a parliament instead of God was a disgrace.
It was this fearful, restrictive atmosphere in the years leading up to 1848 that made revolutionary groups buzz with resentment at the suffocating repression they felt, and outbursts against the established order happened in the years prior. Poles in the Russian Empire protested the rollback on the rights they had been given in 1815 and mounted an insurrection in 1830. There was a failed rebellion in Naples against Habsburg domination in Italy in 1821 (Austria had direct rule over Venice and Lombardy, and the Kaiser had either his relatives ruling over the other duchies or had guaranteed political submission from all the Italian states except the Kindgdom of Sardinia).
This is the setting in which a new generation of prospective revolutionaries found themselves in. They dreamed of a new Europe with guaranteed individual freedoms, and fancied themselves the arbiters of the new age to come. These people became full-time activists, and boogeymen to the statesmen that toiled to sustain the rigid social order of Europe.
Was it one sprawling movement? It would have liked to be. Giuseppe Mazzini, perhaps the most central figure of Italian nationalism next to Garibaldi, founded Young Italy, an organization composed of Italian liberals under 40 who wished for an Italian republic. Afterwards Mazzini attempted to expand the revolutionary network by founding Young Europe with the help of his like minded Polish and German colleagues, and although it didn't become a tangible organization it inspired the formation of Young Germany, Young Poland, Young Ireland, etc.
So we have the ideologues, now to add the missing ingredients.
Many people could be said to be sympathetic to the revolutionaries and their demands, but they themselves weren't willing to participate in an insurrection. This gradually changed when the states, in order to suppress revolutionary activity, clamped down on benign middle class activities. Education in one's native tongue was ended, as were public meetings or cultural clubs, which alienated those middle class citizens who were not particularly nationalistic but began to feel the sting of government censorship and made liberal arguments more palatable.
Apart from that was the upheaval that the industrial revolution was causing. Peasants had access to less and less land and resources that they traditionally had had a right to as the land was seized for industrial development, and had little choice but to either move to the cities to try to find some source of meager income to survive from, or tried to live from the patches of land they had left, sometimes supplementing their income by stealing food or other goods. (It was during this time period that a young Karl Marx would write in the Rheinische Zeitung, taking the side of the peasantry being arrested for stealing wood in Rhineland province)
And in the city, where industrial output was sporadic and therefore not dependable for a living wage, the workers found themselves living in overcrowded spaces, exposed to the bitter cold of winter and not always being able to meet their needs.
To make matters worse, the decade saw the rise of harvest failures in grain and potato, and triggered the famous famine in Ireland. With no staple foods available many began to starve. Food riots took place in the large cities, and the recession caused by the crisis meant that demand for manufactured goods fell, which meant that factory workers were laid off in the thousands, which meant that they then had no money to spend on goods, and with no social safety net fell into destitution.
Thus the middle and lower classes had a shared interest in the toppling of the old order, and found themselves especially energized due to the complete lack of interest on the side of the state for reform, and the force which it utilized in suppressing dissent.
The tensions had been building for years, the causes were similar across Europe, and though I wouldn't say that the uprisings in the various states were strongly linked, I would definitely agree with the assertion that one successful revolution inspired another.
I'm not a historian, and got this information mostly from Mike Rapport's 1848: Year of Revolution and from what I can remember from Marx's 18th Brumaire of Louis-Napoleon