The "five mindfulness trainings" obviously correspond to the traditional "five precepts".
So you can find more (by other authors) on that subject by searching for "third precept", for example Buddhism and Sex.
A lot of what what "appropriate ways" means is explained fairly clearly in the paragraph you referenced, i.e.
Aware of the suffering caused by sexual misconduct, I am committed to cultivating responsibility and learning ways to protect the safety and integrity of individuals, couples, families, and society. Knowing that sexual desire is not love, and that sexual activity motivated by craving always harms myself as well as others, I am determined not to engage in sexual relations without true love and a deep, long-term commitment made known to my family and friends. I will do everything in my power to protect children from sexual abuse and to prevent couples and families from being broken by sexual misconduct. Seeing that body and mind are one, I am committed to learning appropriate ways to take care of my sexual energy and cultivating loving kindness, compassion, joy and inclusiveness – which are the four basic elements of true love – for my greater happiness and the greater happiness of others. Practicing true love, we know that we will continue beautifully into the future.
The simplest definition of "appropriate ways" is "not inappropriate".
Examples of "inappropriate" are described in AN 10.176:
He gets sexually involved with those who are protected by their mothers, their fathers, their brothers, their sisters, their relatives, or their Dhamma; those with husbands, those who entail punishments, or even those crowned with flowers by another man.
In other words, don't break existing families. Like, first of all, do no harm.
Some people interpret this as meaning that, according to the letter of the law, casual sexual relations with otherwise-unattached (i.e. unmarried, independent) partners (or prostitutes) is OK: not wise, necessarily; and ultimately dissatisfactory; but at least not immoral, not breaking the third precept.
But Thich Nhat Hanh goes further than that, when he says, "true love and a deep, long-term commitment made known to my family and friends", which sounds to me like marriage (or celibacy).
He also says that "sexual desire is not love, and that sexual activity motivated by craving always harms": so "appropriate ways" means consequent to a loving relationship, in which in which sexual desire is not mistaken for love.
FYI this answer summarized some guidelines for choosing a marriage partner.
To summarize the paragraph:
Buddhist notions of virtue (sila), for each of the five precepts, equate virtue with protecting or freeing everyone from harm; and freeing everyone includes or results in a share of that freedom yourself:
Furthermore, abandoning illicit sex, the disciple of the noble ones abstains from illicit sex. In doing so, he gives freedom from danger, freedom from animosity, freedom from oppression to limitless numbers of beings. In giving freedom from danger, freedom from animosity, freedom from oppression to limitless numbers of beings, he gains a share in limitless freedom from danger, freedom from animosity, and freedom from oppression. This is the third gift...
One of the famous summaries of Buddhism is from the Dhammapada:
Verse 183: Not to do evil, to cultivate merit, to purify one's mind - this is the Teaching of the Buddhas.
"Not doing evil" ranks highly, is important.
"Abstaining from (harmful or evil) sexual misconduct" is part of the five precepts, which is part of the first training.
It's not only a negative (absence of harm), it's also a way towards a positive.