How do Catholics describe "eternal generation"? It seems to me that "eternal generation" is an oxymoron:


  "a combination of contradictory or incongruous words (as cruel
  kindness); broadly :  something (as a concept) that is made up of
  contradictory or incongruous elements"


It seems to me that "generation" requires at least a single step:


  a :  the action or process of producing offspring :  procreation b : 
  the process of coming or bringing into being  c
  :  origination by a generating process :  production; especially : 
  formation of a geometric figure by motion of another


Do they say:


God and Jesus both existed eternally with Jesus "describable" as a son, begotten, etc. but with no actual, literal birthing having occurred?
the begetting of Jesus occurred so long ago as to be for all intents and purposes to still be considered "eternally so"?
it is a "mystery beyond human comprehension" (as the Trinity in general is often described)? 


Or do they simply use the term without explanation of the contradiction?
The English word “generation” is derived from the Latin word generatio, which is used in the Latin Vulgate to translate the Greek word γένεσις that occurs in the Greek New Testament.
For example, in Matt. 1:1–2, it is written,

1 The book of the generation of Jesus Christ, the son of David, the son of Abraham. 2 Abraham begat Isaac; and Isaac begat Jacob; and Jacob begat Judas and his brethren;  KJV, 1769
Α Βίβλος γενέσεως Ἰησοῦ Χριστοῦ, υἱοῦ Δαβὶδ, υἱοῦ Ἀβραάμ Β Ἀβραὰμ ἐγέννησεν τὸν Ἰσαάκ Ἰσαὰκ δὲ ἐγέννησεν τὸν Ἰακώβ Ἰακὼβ δὲ ἐγέννησεν τὸν Ἰούδαν καὶ τοὺς ἀδελφοὺς αὐτοῦ TR, 1550

Not only did I embolden generation and γενέσεως, but also begat and ἐγέννησεν. One must note that ἐγέννησεν, a conjugation of the lemma γεννῶ (contraction of γεννάω), is related to the noun γένεσις (and thus the genitive case, singular number declension γενέσεως) by the stem γεν-. While the KJV translates ἐγέννησεν as “begat,” it could also be translated as “engendered,” thus retaining the gen- stem in English.
To beget or engender someone is simply to father them. We understand this temporal generation according to our own human nature. During human generation and subsequent birth, a human is made and comes into existence.
In endeavoring to understand the eternal generation of God the Son, some erroneously transfer those same human processes to the Holy Trinity. They reason that, if we were made and came into existence by our own generation by our own parents, then God the Son must have also been made and come into existence by his eternal generation by God the Father.
The problem with this reasoning is that our parents, being human, are mutable creatures, while God the Father is the immutable Creator. Whenever human parents conceive a fetus, the fetus can never be an exact image and representation of its parents—a perfect clone, if you will. Not only are there two parents, and the fetus cannot receive the entire genetic material of each parent, but each parent’s genetic material has endured decay and mutation during the parent’s lifetime. It is absolutely impossible (zero probability) for a child to be an exact “twin” (clone) of its parents.
On the other hand, God the Son is “the image of the invisible God.”1 This is not merely analogous to someone taking a photograph of someone else and looking at the photograph saying, “This is really a nice photo of you!” First, the photograph is not living. Secondly, it is corruptible and can be destroyed. On the other hand, God the Son who is the image of the invisible God is eternal and immutable, “the same yesterday, today, and forever.”2 Only God is immutable since He alone is uncreated. All else that is created is mutable.
In Dialogue with Trypho the Jew, Justin Martyr wrote,3

For those things which exist after God, or shall exist at some time, these have a corruptible nature, and are such as may be both utterly destroyed and no longer exist; for God alone is unoriginated and incorruptible, and therefore, He is God, but all other things after Him are originated and corruptible.
ὅσα γάρ ἐστι μετὰ τὸν θεὸν ἢ ἔσται ποτέ, ταῦτα φύσιν φθαρτὴν ἔχειν, καὶ οἷά τε ἐξαφανισθῆναι καὶ μὴ εἶναι ἔτι· μόνος γὰρ ἀγέννητος καὶ ἄφθαρτος ὁ θεὸς καὶ διὰ τοῦτο θεός ἐστι, τὰ δὲ λοιπὰ πάντα μετὰ τοῦτον γεννητὰ καὶ φθαρτά.

The eternal generation of the Lord Jesus Christ is alluded to in scripture in John 8:42, wherein the Lord Jesus Christ states, «ἐκ τοῦ θεοῦ ἐξῆλθον»—“I came out of God.” This particular phrase consisting of the verb ἐξέρχομαι in combination with the preposition ἐκ suggests being born or generated.4
Henry Alford wrote,5

ἥκω conveys the result of ἐξῆλθον, as Meyer; who also remarks that mere sending will not exhaust ἐξῆλθον, which must be taken metaphysically, of the proceeding forth of the Eternal Son from the essence of the Father.

As far as how this eternal generation and procession occurred in eternity, there is no possible way for any human to conceive of such thoughts. It is beyond our understanding, for as we do not even understand the complex physiological processes and operations of our own bodies, how could we possibly understand something supernatural and extraordinary as the eternal generation?
The best means we have of understanding the eternal generation is limited to analogies.6 As we do not truly comprehend the very essence or existence of God, we certainly cannot comprehend His operations, including the creation of the universe, and especially, the eternal generation of His Son.

References
Alford, Henry. The Greek Testament. Vol. 1. Boston: Lee, 1878.
S. Justinus Philosophus et Martyr. Πρὸς Τρύφωνα Ἰουδαῖον Διάλογος (“Dialogue with Trypho the Jew”). Patrologiæ Cursus Completus: Series Græca. Ed. Migne, Jacques Paul. Vol. 6. Petit-Montrouge: Imprimerie Catholique, 1857.
Footnotes
1 Col. 1:15
2 Heb. 13:8
3 Ch. V, p. 488
4 cp. Gen. 15:4, 35:11
5 p. 797
6 Justin Martyr used the analogy of a fire kindling another fire yet not being diminished in intensity. See his Dialogue with Trypho the Jew, Ch. LXI and CXXVIII.