Images and memes like this always pop up from time to time. How close were the Vietnamese to what we would call a modern army?
It's important to differentiate between the two communist Vietnamese forces fighting the South Vietnamese, the United States, and their allies.
The People's Army of Vietnam (PAVN), were the army of the Democratic Republic of Vietnam (North Vietnam). Equipped and trained by the People's Republic of China and the Soviet Union, the PAVN were a top-rate army in Southeast Asia.
The National Liberation Front (NLF), also known as the Viet Cong, was the armed insurgency fighting within South Vietnam. These soldiers and guerrillas were largely Northern-led and staffed by Southerners until the Tet Offensive in 1968, which largely destroyed the Viet Cong as a fighting force. From then on, the Viet Cong would consist of a great many Northerners who had infiltrated south via the Ho Chi Minh trail.
Early war combat was largely small-unit affairs, but while a Viet Cong ambush may have been perceived by American advisors as "man in black pajamas," the Viet Cong had a clearly defined organizational structure and units. Many of the Saigon and rural terrorist attacks were executed by underground cells of Viet Cong, not generally isolated, individual attacks.
Small Arms:
Early war, the PAVN and Viet Cong could be seen using World War II vintage small arms, with many having been captured from French or South Vietnamese military stocks. Lots of bolt-action Mosin Nagants, semi-automatic SKS rifles, and Soviet machine guns. The use of the AK pattern rifles was rare. There were also few main-force PAVN units in South Vietnam, and so many of the battles in the early war were fought against Viet Cong units, generally battalion-sized and under.
By the introduction of US combat forces in the mid-60's, more PAVN regiments began to enter into South Vietnam. Division sized units were still relatively rare to be encountered by the South Vietnamese and the Americans, however. By mid-war, the PAVN had reequipped with the AK pattern rifle from Soviet and Chinese military aid, which gave them the small arms advantage over the South Vietnamese, who in the mid-60's were still largely fighting with M1 Garand rifles and M2 carbines from World War II. RPGs also began to proliferate, primarily the RPG-2 model.
By the late 60's, more Viet Cong units began receiving AK pattern rifles, though they often still just used whatever they could ge their hands on. By 1968, much of the ARVN had received M16 rifles, though Popular and Regional Forces remained using World War II vintage firearms.
Frontline communist Vietnamese soldiers generally enjoyed arms parity or advantage to the South Vietnamese and Americans for a great deal of the war.
Heavy weapons:
While the North Vietnamese never operated fixed wing aircraft and helicopters in South Vietnam, they possessed a great deal of anti-aircraft weaponry to include both AAA and SAMs. 14.5mm KPV machine guns and 12.7mm DShK machine guns served as excellent anti-helicopter weapons. By late war, the North had begun to use shoulder-fired SAMs to great effect against the South Vietnamese. Shoulder-fired RPGs were used as both anti-helicopter weapons and direct-fire infantry weapons as well.
Training:
The PAVN received training from in-country Soviet and Chinese military advisors. Organized into divisions, the PAVN were every bit of a modern army as the South Vietnamese were. By late war, they were outgunning many of the South Vietnamese divisions they were attacking, save for the airpower advantage that the United States (and South Vietnamese to a lesser extent) brought to the table. Importantly, the Chinese had military experience fighting the Americans during the Korean War, and so it was not just theory being taught to the Vietnamese.
The Viet Cong were largely trained, led, and controlled by the North Vietnamese. Although famed for their guerrilla and terrorist attacks in the South, the Viet Cong also attempted to organize itself into conventional battalion and regimental sized units, though many were completely wiped out in the Tet Offensive, after which the Viet Cong were not able to conduct large scale conventional assaults again, leaving that for the massive number of PAVN conventional forces pouring into South Vietnam. By late war, Viet Cong units were relegated to blocking or harassing missions, letting the PAVN undertake the main battles.
Conventional tactics:
Late war combat in Vietnam was characterized by massive conventional assaults, primarily the 1972 Easter Offensive and the 1975 Spring Offensive. In those two campaigns, the North Vietnamese utilized combined arms tactics, with Soviet produced main battle tanks accompanied by mixed infantry. The myth of the "rice farmer" enemy had transformed into a competent, conventionally armed modern soldier. North Vietnamese soldiers were downing South Vietnamese gunships with SAMs up until the ceasefire was declared on April 30, 1975, and main battle tanks—T-54/55s—were being destroyed by LAW antitank rocket launchers in downtown Saigon. In order to facilitate these long-distance offensives, the PAVN had largely perfect the logistical trail through Laos and Cambodia. What was once a simple dirt trail through the jungle (which is oftentimes still the popular memory), the Ho Chi Minh trail by the end of the war was a multi-laned, paved highway that could handle tracked and wheeled heavy vehicles like APCs and tanks. It even had an oil pipeline running alongside it.
While there is some truth to the idea that some communist forces in Vietnam were raised from the peasantry, it is an over-romanticization of the mid- and late-war situations. Many North Vietnamese and Viet Cong officers were fighting the Japanese and the French—decades of field experience on their home turf. They were not "rice farmers." The massive conventional attacks at the end of the war are the proof that the North Vietnamese were a modern army to be reckoned with.