Whether undertaking directed or undirected meditation, the preparation for and beginning of meditation is the same: there is the preparation for readiness, and the flexing of the mind.
Readiness is achieved by practicing waiting - without anticipation.
When you wait for a bus to arrive, there is nothing you can do to make the bus arrive sooner (or later). There is nothing to do, except to be at the bus stop. A person waiting for a bus does not spend the time waiting for the bus anticipating the coming of the bus, but will simply make sure they are ready to board the bus when it arrives - and then divert themselves by reading a book, playing a game, or listening to music, talking with friends and neighbors, watching traffic, thinking about what they have done or will do, or thinking about nothing at all.
In the same way, a person preparing for meditation should simply make sure they are ready to begin meditation, whether directed or undirected meditation. They might study the Dharma, or perform Artha Yoga or Kama Yoga, they might perform some Kirtan or Sankirtan Yoga, they might engage in the pleasant conversation of Satsang, observe the world passing them by, in the study of logic, the nature of reality - or purposefully doing nothing at all.
A person who is prepared for meditation will then flex their minds. This is achieved by exerting control over emotion, instinct, cogitation, and numerous other mental functions. As an athlete will stretch all their muscles before exerting themselves, so should every part of the mind be flexed. Feeling every emotion, thinking every thought, aware of every sensation delivered to the mind by eyes, ears, nose, mouth, tongue and skin, aware of every process of understanding those sensations through consciousness, in profound Samadhi, make your mind flexible by flexing it.
Feel the limits of your mind: exert your mind where it is weak, strengthen it: perhaps there is an emotion which is difficult to bear today? Or a thought which is difficult to comprehend? Many people struggle with the concepts of infinity, or the asymptotic and koan-like contradictions of negatory logic, or even the nature of existence. Think upon a koan, or a mantra, extend your mind to the limits of its ability - having thus flexed to the limit, you are ready for meditation.
Put another way, arriving at the state of directed or undirected meditation is the same: consider, the vehicles of a Shaivist, who will typically employ undirected meditation, and Vishnaivist, who will typically employ directed meditation, are the same: Garuda is Shiva*; Nandi is Shiva.
In the Ramayana, Hanuman took the form of Panchamukha Hanuman, a combined Avatar of Vishnu and Shiva, with five faces: Hanuman, Hayagriva, Narasimha, Garuda and Varaha (Hanuman used the five faces in different directions to blow air and extinguish the lamps required to destroy Ahiravana). Hanuman is the Avatar of Shiva, and thus at that moment, Hanuman-Garuda can be seen also as Shiva-Garuda. The act of Samadhi is the vehicles merging, together with their passengers.
Waiting for the bus quickly becomes Samadhi with the bus when the bus (vehicle) is boarded.