Q:

What are the Three Trainings and how are they practical?

What are the Three Trainings and how are they practical?
Specifically how does one practice them?

A:

The threefold training (Pali: sikkha) consists of: morality (sila); concentration (samadhi); and wisdom (panna).
Sikkha is meant to conquer and eradicate the defilements (kilesas).
Visuddhimagga XXII,49

'The defilements are the ten states, namely: greed; hate; delusion;
  conceit; false view; uncertainty; stiffness of mind; agitation;
  conciencelessness, shamelessness. They are so called because they are
  themselves defiled and because they defile their associated states.'

Each of those defilements has 3 stages (bhumi) which are identical to the 3 stages of consciousness (latent - manifested - action).

the latent stage = anusaya-bhumi
the manifest stage = pariyutthana-bhumi
the action stage = vitikkama-bhumi

Through the threefold training, it is possible to conquer and eradicate these defilements in the 3 subsequent stages: sila-sikkha; samadhi-sikkha; and panna-sikkha.
The training itself is a strict personal affair: Purity and impurity depend on oneself. No one can purify another (Dhammapada).

A:

The Three (Higher) Trainings are:
Ethics
Concentration
Wisdom
The practice of ETHICS entails abandoning negative actions of body, speech and mind (such as killing, stealing, lying, sexual misconduct, intoxicating the body, harmful speech, greed, etc). And cultivating virtuous actions of body, speech and mind (generosity, patience, gentle speech, etc). 
The practice of CONCENTRATION entails developing single-pointed attention on a meditative object (such as the sensations of the breath, a mental image, thoughts and the space of the mind, etc) by cultivating relaxation, stability and vividness. There are 9 stages for the this practice (shamatha) and the culmination is a refined mind that experiences bliss, clarity and non-conceptuality. At this point you are able to focus your attention effortless for long periods (4 hours or more) without any distraction or internal chit-chat, this state is called samadhi. 
The practice of WISDOM entails, gaining insight into the nature of reality, this means understanding experientially and not only conceptually how all phenomena and oneself exist. Everything exists as an interdependent matrix of causes and effects, and everything is empty of inherent existence. 
The first step is to begin practicing the Four Applications of Mindfulness:
Applied Mindfulness to the body, feelings, mental events and phenomena. These practices imply not only being mindful of the body sensations, thoughts, etc, but also to develop wisdom by questioning if these things exist as we perceive them or if they are impermanent, interdependent and lacking an inherent, real, solid existence. After becoming good at these practices you can also practice analytical meditation, debate, and Dream yoga to start questioning the solidity of what you call reality.These practices are called Vipashyana and one applies them also to the I, until one finds that one doesn't exist as an independent ego, but as a matrix of interrelated phenomena and that we also lack inherent existence. There's a risk here to think we don't exist at all and becoming depressed or nihilistic, so it's important to practice also Dzogchen, Mahamudra or similar practice to understand and realize that we are pure awareness and by recognizing this primordial consciousness we transcend the concepts of existence and non-existence and we become enlightened. 
This insights can only be sustained if you have achieved single-pointed concentration (shamatha) first, otherwise with an unbalanced, wandering mind trying to develop wisdom is not possible. And concentration can only be achieved if one lives an ethical way of life, because a mind that is filled with mental afflictions such as anger, craving, greed, attachment, ignorance, arrogance, etc, is a wandering mind unable to find peace and develop concentration, furthermore an afflictive mind is ignorant and unable to develop wisdom. 

