I am not so knowledgeable about answering this question. My impression is, at least the Pali Suttas, do not contain many approaches to metta meditation.
Some basic Pali Sutta passages about metta, in increasing detail, are:
Meditate on love. For when you meditate on love any ill will will be given up.
Seeing that the hindrances have been given up in them, joy springs up. Being joyful, rapture springs up. When the mind is full of rapture, the body becomes tranquil. When the body is tranquil, they feel bliss. And when blissful, the mind becomes immersed.They meditate spreading a heart full of love to one direction, and to the second, and to the third, and to the fourth. In the same way above, below, across, everywhere, all around, they spread a heart full of love to the whole world—abundant, expansive, limitless, free of enmity and ill will.
Karaniya Metta Sutta
In Theravada Buddhism, Chapter IX (page 291) the Visuddhimagga is a popular manual.