Hitler sent 20 Junkers-S2 to airlift the army from Africa to mainland rebel-held Spain near Cadiz. Mussolini sent over 10 of his bombers to destroy the Republican defences on the coast. The airlift was a success as within two weeks, Franco's Africanistas were in Spain and marching towards Madrid. If it had not been because of this, the rebel army would have been stranded form much longer in Spanish Morocco, so it was vital in this occasion. It's likely though that Franco finally organised themselves. On the day of the coup, Franco was taken from the Conary Islands to Spanish Morocco in a British-piloted plane which received much less attention than if he had gone on a Spanish one which might have been prevented to have. Franco's ability as a commander was important for the whole war and therefore foreign support did play an essential part too.
On the mainland Spain, 30.000 Portuguese troops were sent by Salazar to assist Franco. Mussolini dents 60.000 soldiers in the CVT which was apparently a volunteer army. Nazi Germany helped Nationalists Spain with supplies and sent the Cordon Legion. The foreign armies though never played a huge part in the capture of important cities except some like Malaga. Franco wanted his army to take all the credit of capturing these cities. The Condor Legion destroyed the whole of the town of Guernica in 1937 but this was not a significant victory as the town was not strategically important. Foreign troops and volunteers did play a part in the success of the Nationalists in the Spanish Civil War but it would be inaccurate to say that it was mainly due to this foreign support that Franco won.
Supplies sent by Nazi Germany such as tanks, weapons, advisers and money played a more important part than Solozar's troops for example. American companies sold supplies to the Nationalists too. Foreign support though did them win the war but it was not mainly because of it that it was won. The fact that the Nationalists had a unified chain of command was extremely important. The Republicans on the other hand had divisions between themselves because of the militias and the various political groups such as the anarchists and communists who even fight between each other orders were debuted on the front line which led to considerable problems. The Republicans did not have the military advantage that the Nationalists had which was to have core and expended Africanistas.
To say that the success of the Nationalist was mainly due to foreign support is wrong, because the soldiers who fought on the ground were the main reason of their victory, but we also can't reject the fact that military equipments played a huge part as well. That's also was a reason why Republicans didn't win, because Soviet Union had worse military equipment than Germany and Italy. As well Russians always were asking Republicans to repay the loans as soon as possible, while Germany never put so much much pressure on Nationalists. As I wrote earlier there were disputes between Republicans themselves. So if we were looking at all the reasons why the Nationalists won, the reason of foreign support would be on of the main reason.