How do I practice ' see things as they are'?

It is not ''to see things as they really are'', contrary to the stock translation.

it is:

• once you want to stop experiencing once and for all misery,
• to see once and for all ''how things arise and go away''
• which means to see once and for all they are mediocre, pathetic and unreliable, ie dukkha
• which means seeing once and for all they are not ''I nor mine'', ie not your business not your story, ie anatta
• which means experiencing once and for all dissatisfaction with them and not to even touch them
• which means experiencing once and for all disinterest with them
• which means nirvana.

The first step to be sucked into this spiral is

• to ''''''''be moral'''''' like some puthujjana say, meaning not causing drama over mundanities with other people until you have no regrets nor remorse nor worry about their mundane activities,
• once there is no worry over the mundane activities created and cared by those people, you are left alone to have time to experience the ''tireless energy'' and joy of the jhanas,
• once there is this joy, energy, relaxation, you become concentrated and have most of the ''''seven factors of Enlightenment'''''' which I copy paste here

** - Mindfulness (sati).  
 - Investigation of the nature of reality (dhamma vicaya).**
 - Energy (viriya) also determination
 - Joy or rapture (pīti)
 - Relaxation or tranquility (passaddhi) 
 - Concentration, clear awareness (samādhi)  
 - Equanimity (upekkha).

Now to get to the point of no return, you must develop the first two, otherwise you are stuck at the jahnas like the hindus. It turns out what remains is precisely remembering the doctrine and investigating it, which exactly means the first list above:

• once you want to stop experiencing once and for all misery,
• to see once and for all ''how things arise and go away''
• which means to see once and for all they are mediocre, pathetic and unreliable, ie dukkha
• which means seeing once and for all they are not ''I nor mine'', ie not your business not your story, ie anatta
• which means experiencing once and for all dissatisfaction with them and not to even touch them
• which means experiencing once and for all disinterest with them
• which means nirvana.

You know black hole because you fluently understand the knowledge of the relation of physical&chemical properties about black hole. It doesn't mean you have seen black hole.

"Seeing things as they are" is the same. You know their paṭiccasamuppāda (causes) in every time before you know them (effects) directly.

You think some one mad because of their properties, so you never think the dead body is mad. The same way, the practitioner think clinging-aggregates are "impermanent, suffering, anattā" because they aggregates depending on clinging-paṭiccasamuppāda. So, without paṭiccasamuppāda 12, the practitioner can not see impermanent-characteristic, suffering-characteristic, anattā-characteristic" of "impermanent-aggregates, suffering-aggregates, anattā-aggregates".

This is the reason why the practitioner can meditate sammasana-ñāṇa(realizing everything have 3 characteristics) after paccayapariggahañāṇa (realizing paṭiccasamuppāda/paṭṭhāna).

So, to practice "Seeing things as they are", you have to practice to see everything in paṭiccasamuppāda style. But before that step, you have to make sure that you having good enough adhi-sīla & adhi-samādhi (sīlavisuddhi&cittavisuddhi).

See, KN Paṭisambhidāmagga Dhammaṭṭhitiñāṇaniddesa & Visuddhimagga Paccayapariggahañāṇaniddesa. Both path of them describing yathābhūtañāṇa, directly:

25. The knowledge that has been established by the overcoming of doubt about the three periods of time by discerning the conditions (paccayapariggaha[ñāṇa]) of mentality-materiality according to the various methods should be understood as “purification by overcoming doubt (kaṅkhāvitaraṇavisuddhi).” Other terms for it are “knowledge of the relations of states (dhammaṭṭhiti)” and “correct knowledge (yathābhūtañāṇa)” and “right vision (sammādassana).”

26. For this is said: “Understanding of discernment of conditions thus, ‘Ignorance is a condition, formations are conditionally arisen, and both these states are conditionally arisen,’ is knowledge of the causal relationship of states” (Paþis I 50). And:

...

“When he brings to mind as impermanent, he correctly knows and sees the sign. Hence ‘right seeing’ is said. Thus, by inference from that, all formations are clearly seen as impermanent. Herein doubt is abandoned. When he brings to mind as painful, he correctly knows and sees occurrence. Hence ... When he brings to mind as not-self, he correctly knows and sees the sign and occurrence. Hence ‘right seeing’ is said. Thus, by inference from that, all states are clearly seen as not-self. Herein doubt is abandoned.

Another, I also describe yathābhūta in this answer: https://buddhism.stackexchange.com/a/26699/10100

Craving, delight & seductive qualities beguile the mind; including when seeing radiant monks & Buddhas. To see things as they are requires a pure mind without defilements; without craving.

Its a chicken vs egg scenario. Enough defilements must be cleansed so seeing things as they are can put an end to defilements. , Mentality ('nama') is just as or even more beguiling than physicality ('rupa'). For example, the so-called 'beauty' of a female form is more than mere physicality. The mind of the woman is also exuding an enticing quality.

Thus, to see things as they are, both internal & external bodies & minds must be seen as merely that: mental (nama) elements & physical (rupa) elements.

The elements are listed in MN 115. Viewing external objects as mere mentality phenomena (nama) and physical phenomena (rupa) is described in SN 12.19.

In my understanding of the explanations I received:

As many Buddhist concepts, "seeing things as they are" is a pointer to something happening in real life, but not necessarily in a sense we assume. Its meaning is more practical than strictly technical.

Most of the time we are "in our heads". We have so many preconceptions, thoughts, and inner chatter going on, that we can barely see what's going on in the real world. Instead, our vision is limited by our thoughts and preconceptions to such a degree that we barely notice things outside of our frame of reference. We tend to ignore them for two reasons: either

A) in our frame of mind they are not cohesive phenomena, they seem illogical (because we don't understand their inner logic) - and so we tend to ignore them as noise, or

B) they go against our emotional attachment to some sort of theory or ideology, and so we semi-subconsciously dismiss them as fake / illusory / insignificant.

When we learn to suspend our judgement and lay aside our attachments and preconceptions (this is what Mahayana's realization of Emptiness entails in practice), and stop our never-ending inner-monologue, and lose solidity of this heap of overgeneralizations we call "ego" -- then and only then we start seeing things "as they are".

In my experience with it, this vision liberated from preconceptions can be allegorically called "quantum" or "multidimensional". Because we are not limited to one theory and one interpretation of what's going on, we see them all, or rather, we directly see the entire "space of interpretations". There is an element of ambiguity, but it's not regular ambiguity which is hazy vision - instead it is a very clear kind of ambiguity.

It's a very practical, very direct kind of vision. We are simply not in our heads, are eyes are open and we really look around, and see things we have not seen before.

This is the critical point of the explanation.

And then on top of that, as we develop prajna, we begin to "see" "hidden connections" between things. These are not as much some magic properties as abstract relationships of (latent) influence and causation.

Combination of this "quantum" vision and seeing the latent influences is called "seeing things as they are" - in my understanding.