How did the Marines operate in Vietnam?

Before WW I they were primarily used as shore parties and guards on warships and Naval facilities. With the steam age they were given the additional task of manning one of the guns.

During WW I the US needed a couple of quick divisions to ship to France as quickly as possible. They rounded up Army Unites from scattered forts around the country and crated the First Division, and rounded up Marines from the various duties they were performing (often guarding ship-yards and Navel Stations) and created two of the Regiments of the Second Division. The Marines fought as standard infantry in France. They got a lot of press, and POd the Army off as showboats (not that they didn't deserve the credit).

During WW II they were organized into their own Division sized units, and employed as landing parties by the Navy in their push across the Central Pacific. They were supported by Naval Warships and air in addition to their own close support aircraft. But they were never as completely on their own as you indicate.

After the war they developed the specialty of over the beach assault and were often deployed as self-contained Regimental Combat teams. During Korea they were used as firemen to plug holes in the line around Pusan until MacArthur pulled them all out of the line and used them to invade Inchon. For the rest of that war they pretty much operated as standard infantry calling on any air-support (Marine, Navy, or AF) available when needed.

The first Marines were deployed in Vietnam to secure the big Air Base at Da Nang in the Northern part of South Vietnam. There was a lot of speculation at the time that, because they were considered shock troops, the US might be building up for an invasion of North Vietnam. As their duties expanded from security to ground operations they fell into a routine not unlike that of WW I and Korea where they operated as standard infantry. They were supported by their own air-groups, but could (and did) call on Navy and AF aircraft when necessary.

After WW II, Korea, and Vietnam there were a lot of calls to roll the Marines into the Army, but the Navy (and Marines) have successfully fought off those attempts. In the war on terror the Marines have been deployed in Iraq and Afghanistan in much the same way as WW I, Korea, and Vietnam. They are being used as infantry far from the nearest body of water. But they still get somewhat more intense training than the standard Army troops, and are still considered shock troops and amphibian warfare specialists. They can still be deployed very quickly as self-contained Regimental Combat teams which make them ideal for quick deployment to hot spots like confronting the Iraqis in Saudi Arabia before the big buildup of Army troops in the early 90s.

Give me one operation where they have operated totally unsupported by another branch.....

Same goes for the Army