Nixon's primary focus of policy that sought to end the Vietnam conflict was the seeking out of diplomatic dialogue between both sides. Nixon and Secretary of State Kissinger actively sought to open channels with the Vietnamese in order to draft parameters and limitations that could form the basis of a lasting peace in the region. This is something that his predecessor, President Johnson never could nor sought to do. In terms of policies that seemed to increase the involvement, Nixon increased the bombing of the Vietnam nation and also saw it spill over into Cambodia and other neighboring nations. This helped to cause a bit of a tension, or credibility gap, between Nixon and the American people, for on one hand there were active attempts and dialogue that sought to end the war while at the same time there were actions that were intended to increase the scope and impact of the war.
Nixon was elected on a policy idea of getting us out of Vietnam, while still winning the war - no easy trick. So he lessened our involvement almost immediately after taking office by beginning to phase out our troop strength there. In his first term Nixon reduced the total number of American troops in Vietnam by nearly two thirds, at the same time as those troops were heavily engaged in offensive operations.
He did widen the war into Cambodia at one point, and he also authorized vastly increased bombing missions over North Vietnam, Cambodia and Laos - essentially all of French Indochina. His idea was to "bomb them to the peace table" so they would cut a deal with the US. In part this worked, but it was definitely an escalation in the war.
The major example of a policy that seemed to lessen US involvement in the Vietnam War was Nixon's policy of "Vietnamization." In this policy, the US was supposed to be handing over responsibility for the war to the Vietnamese themselves.
In terms of things that seemed to make the US get more involved, Nixon did some things that seemed to widen the war. For example, he ordered the invasion of Cambodia, which had previously been off limits. He also really intensified bombing of North Vietnam. By intensifying and spreading the war, he seemed to be pushing for more US involvement.