I've found that by simply maintaining mindfulness of the body and attention on the breath, which in itself is a sort of applied and sustained attention, boosted by an attitude of relinquishment, the hindrances are naturally restrained, resulting in a calm and inwardly settled state. This calm naturally matures into a full experience of vivekajam-piti-sukha as the meditation is continued. This bit from the Samaññaphala Sutta describes the progression quite well: "Seeing that they (the hindrances) have been abandoned within him, he becomes glad. Glad, he becomes enraptured. Enraptured(piti), his body grows tranquil. His body tranquil, he is sensitive to pleasure(sukha). Feeling pleasure, his mind becomes concentrated." Since the mind and body are mutually pervaded with mindfulness, any piti or sukha that arises in one simultaneously fills the other, nevertheless often times some intentional effort, that is, vitakka and vicara, applied and sustained attention, is needed to maximize and stabilize it.
It feels to me rather like putting your hand into a blob of paint (vitakka, applied attention) and spreading the paint out from that point (vicara). This comparison leaves something to be desired but it describes fairly well how I experience vitakka and vicara as they act upon pitisukha. In a way, the original vitakka and vicara of sustaining and spreading stable mindfulness throughout the body is simply given another factor to work with, and as mindfulness of the body is cultivated, the resulting pitisukha of the tranquil mind naturally gets spread and strengthened too.
As attention is sustained in this way, pitisukha as well as mindfulness and concentration mutually strengthen each other. The stronger the mindfulness and attention the more secluded and focused the mind, leading to deeper vivekajam-piti-sukha, which leads to stronger concentration and mindfulness, and a sort of feedback loop of factors is established. When the mind and body are full of stable awareness and pitisukha strong all throughout, the motion of vitakka and vicara can naturally subside since they have fulfilled their purpose in stabilizing absorption, or they can be artificially maintained if the various factors are, albeit pervasive, not strong enough for the degree of concentration desired. Not all factors necessarily arise in the same way in the same degree every time, it seems.