From the implementation paper:
"The algorithm randomly selects as a proposal (in the Metropolis sense) either a new knot (a birth step), removal of a knot (a death step), or a relocation of a knot.
Birth and relocation steps begin by randomly selecting a knot, with equal probabilities, from among all knots in the current knot set. If the proposal involves a birth step, then a location for the potential new knot is randomly selected by first randomly selecting an existing knot and then drawing from a beta distribution centered at that knot. This beta distribution is typically quite tight around its center (with spread controlled by an optional user-defined parameter tau) in order to propose knots that are close to existing knots. The same beta distribution is used to propose a knot relocation (the distribution being centered on the knot to be potentially relocated). As usual, the proposal to add, delete, or relocate is evaluated, and possibly accepted, via the Metropolis-Hastings ratio."
There is pseudocode in the same paper.