Transcendence in Buddhism means to overstep (transcend) some field, to enter another field. Like transcending the field of Infinite Space, to enter the field of infinite consciousness.

Buddhism is not really Universalism - that is to say "to make "one" out of two".
Buddhism is more like "choosing one among two". That is to say, to leave a lower state, to enter a new one. Or again, to "clean" something out of one thing, to arrive at its pristine state (as in cleaning the mind from defilements, and move up to a higher state). However, it is always about abandoning something, to enter a new or higher state. 


As usual, use the visual aid .


Basically, a "sense-consciousness", is the meeting of the external field (of sensory experience,) [bāhirāni āyatana], with an internal field [ajjhatikāni āyatana].

And that must be avoided, says Buddha.
Because "sense-consciousness" yields "contact"; that is to say the transfer of ownership of the khandhas of NāmaRūpa (rūpa, viññāṇa, saṇkhāra, vedanā & saññā) to the khandhas of Satta.
Like when someone sees a Picasso's painting, and transfers the forms (rūpā), the synergies (saṅkhārā) the feelings (vedanā), the perceptions (saññā) and consciousness (viññāṇā) of Picasso, towards oneself - that is to say towards his/her own khandhas.

What makes possible the "sense-consciousness" is the power associated with the field of sensory experience (āyatana) - that is to say the indriya.

When these powers (indriyāni) are not restrained, they "sensualized", so to speak, the fields of experience. They "empower" the fields of sensory experience.
The more indriya (power), the more sensory experience.
But restraining the indriyāni help reduce the synergy/coaction (saṅkhāra) between the external and internal field of sensory experience.

Where is the transcendence (samatikkamma) in all this?

In Buddhism, by holding back the first component of the synergy/coaction - in this case, the external āyatana - (and as importantly, by looking towards the internal field), one transcends to the second component. In our case, the internal āyatana.
In other words, by choosing to restrain the indriya on the external field, one also prevent the descent of the indriya in the internal āyatana. And there is no "sense-consciousness" - and therefore no contact, feeling, craving, holding, etc.
By doing so, one also transcends to the second component.

So what imports here, is that there is transcendence towards the second component of the synergy (saṅkhāra). That is to say, the internal āyatana.

This applies to the next level.
That is to say, that once someone has transcended the world of the senses (kama loka), one must transcend the world of forms (rūpa loka). Then one must transcend the immaterial world (arūpa loka).

We have seen how one transcends the kama loka.
And that can be summarized by what is required to enter progressively into each of the four jhanās - that is to say, after having been secluded from sensual pleasures (vivicceva kāmehi), and secluded from unproper states (vivicca akusalehi dhammehi), etc. In other words, one is asked to dispense with the previous jhāna (by "cleaning up" some things), so as to enter the next and higher one. 

But how does one transcend the rūpa loka?

1. by the complete transcending of perceptions of Form - (rūpasaññānaṃ samatikkamā).
2. by the vanishing of the perceptions (based) upon the organs of senses (āyatanāni) - (paṭighasaññānaṃ atthaṅgamā).
3. by not striving with the mind (manasa/mano) to the perceptions of manifoldness (lit. (what is) differently than one) - (nānattasaññānaṃ amanasikārā)
4. and being aware that the field of experience (āyatana) of ‘space is boundless’ (ananto ākāsoti).

And how does one transcend the arūpa loka?

By continuing to be aware of and long for the next consecutive āyatana; and transcending the previous one.
Just like it was done, when being aware of the internal āyatanāni in saḷāyatana, and transcending the external āyatanāni.

Here is a cheatsheet for JHANA.