The answer is "sent more troops." There were troops in Vietnam before the 1964 election, but mostly they were either military advisors to the Vietnamese army or guarding air bases. We were at war, but the large, brigade scale deployments didn't start until a few months after LBJ's 1965 inauguration.
Important precursors to involvement were the supposed attacks (now subject to some doubt) by North Vietnamese gunboats on the Maddox and Turner Joy in August 1964, which led to Congressional approval of the Gulf of Tonkin resolution, authorizing large-scale intervention. The direct ground war started with the March 1965 deployment of 3500 Marines and numbers increased rapidly.
In my defense consulting job that I held from 1981-1998, my deputy was a retired navy captain who enjoyed telling a joke: "People warned me that if I voted for Goldwater, there would be a war in Vietnam. So, I voted for Goldwater and sure enough, we got a war in Vietnam."