I'm going to assume you mean the success in the French Indochina wars, as the Viet Minh, founded by Ho Chi Minh in 1941, were only around for that war and the Vietnam Conflict.
via /u/algebrace:
The reason the Viet Minh were fighting the French in the first place was because the French promised them autonomy if they fought the Japanese in WW2 however after WW2 it was straight back to business for the French which angered the Vietnamese
Ho Chi Minh, the nationalist, communist leader who eventually came to lead the Viet Cong, the "final form" persay of the Viet Minh, saw an opportunity to unify the various independence groups in Vietnam under one banner, the Viet Minh. Essentially the Viet Minh was a combination of all the other movements, and thus much stronger. The Viet Minh saw an opportunity to end French rule in 1945 as the Japanese pseudo government was dissolving and assumed that the replanted French officials would be more tolerant to an idea of a free Vietnam. They ended up not enjoying that too much, landed an occupation force in 1946, and the Viet Minh fled to the countryside to wage guerrilla war.
The Viet Minh struggled until 1949, when Chinese Communists broke through the border and were able to supply the Viet Minh with conventional weapons. After they were supplied with weapons they became a formidable force that could stand up to the French. This threat led the French to seek outside help by way of America.
In 1950 the US entered the Korean War, and the Cold War was heating up in a big way. America, who had previously supported Ho's anti-Japanese movements, began to supply the French and actively oppose Ho's rule. When Ho's Viet Minh were directly opposed by the US, it brought support from communist Russia.
So, in a nutshell, they were heavily supplied by communist China, and after support from America was denied, communist Russia as well. This was also a point when France was still getting back on it's feet in the area.
Ho Chi Minh, The Lost Years: 1919-1941 Sophie Quinn-Judge for the formation of the Viet Minh
The Military Art of People's War by Vo Nguyen Giap, which is a fantastic read on the Viet Minh by Ho Chi Minh's right hand man.
Excuse me for my brevity, and if I make any astoundingly bad answers, I'm not an expert but have read a few books that touch on the subject, but thought I'd take a shot as no one has provided an answer as of yet.
If I understand the question correctly you are asking why the Viet Minh were the main liberation organization? The answer depends on from what perspective your asking, but the general answer is that the Viet Minh were an umbrella organization that had received outside support during WWII from all the allies, akin to resistance organizations in other countries under occupation during WWII. The shift towards a specific political ideology didn't occur until later on, after shifts in who was providing outside support allowed or instigated political maneuvering for control. Specifically the introduction of French colonial authorities, the removal of American support for the Viet Minh, and Communist Chinese pressuring the Viet Minh to become more in line with Communist ideology in exchange for heavy weapons and training. This meant that those who advocated other political schools of thought were generally removed from power, moved away from the north, or were killed. The supremacy of Communism wasn't really cemented until after the Tet offensive when the last of the more moderate leaders were killed off in South Vietnam, and the political leadership of the Viet Cong was completely take over by the North Vietnam.
Edit: Clarified answer after rereading the question