Per the AD&D 1e MM, they were like other humanoids1
While Original D&D didn't go into this kind of detail (and thus the question's answer is mu for that edition) it did give us this:
GNOLLS: A cross between Gnomes and Trolls (. . . perhaps, Lord Dunsany
did not really make it all that clear) with +2 morale. Otherwise they
are similar to Hobgoblins, although the Gnoll king and his bodyguard
of from 1-4 will fight as Trolls but lack regenerative power. (Monsters and Treasures, p. 8)
Which leaves us guessing if they even reproduce at all or have to wait for a Troll and a Gnome to feel amorous towards each other.
The AD&D 1e MM treated them the same way as most giant class creatures (which was most of the humanoids plus ogres, ettins, trolls, and giants2).
In the second paragraph of the MM entry on gnolls, we find:
The lair will also contain females and young equal to 50% and 200%
respectively of the number of males present (MM, p. 46)
See this similar entry for goblins
... females and young equal to 60% and 100% respectively of the number of male goblins encountered (MM, p. 47)
And this entry for orcs
... females equal 50% of the number of males, young equal to 100% of
the number of males (MM, p. 76)
Entries for bugbears, hobgoblins and ogres are similar. In that respect, they were what D&D 5e would class as a humanoid like a hobgoblin or an orc, with their lair being populated by mates and young in varying proportions to the male population.
From the above we can infer, with confidence, that they reproduced like other humanoid creatures for that edition.
Yeenoghu was a demon, stats as a monster
It is worth noting that the first exposition on the gnoll deity Yeenoghu he was a "demon lord" in the MM; as a deity, he arrives in a book published three years after the MM, Deities and Demigods but they didn't go into much detail in that entry, telling the DM "see the MM".
The relevant treatment in AD&D 2e's MM:
A gnoll lair will contain between 20 and 200 adult males {snip chief
bit}... in a lair , there will be females equal to half the number of
males. Females are equal to males {snip}. There will also be twice as
many young as there are adults in the lair but they do not fight.
{perhaps females give birth to litters? = my thought}. Gnolls always
have at least 1 slave for every 10 adults in the lair and may have
many more.{snip} They dislike goblins, kobolds, giants, humans,
demi-humans{elves, dwarves, etc} and any type of manual labor.
Looks like standard breeding in this case as well.
From the 3.5 SRD, they are described as something different from the other humanoids:
A gnoll is a nocturnal carnivore, preferring intelligent creatures
for food because they scream more.
As I no longer have my 3.5 MM, I'll leave that there as a pointer to differentiating them from the goblins, orcs, and hobgoblins who are more like humans than gnolls were.
Apparently, 4e had two different kinds of gnolls in it: the demon-corrupted Yeenoghu-worshiping gnolls and the nature-worshiping uncorrupted gnolls. (per @nickl012000, Dragon #367, summarized).
Gnolls were originally created by Yeenoghu from mixing together hyena and fiend ... those gnolls that embrace their demonic heritage breed with cacklefiend hyenas ... they have a ritual where cacklefiend hyenas can devour a living humanoid to birth litters of full-blooded fiends from the devoured person's soul ... there are tribes that reject their demonic heritage to embrace their animalistic heritage instead.
This suggests that two ways to create / reproduce gnolls were in play in that edition. This leads us to ...
It might be both ways in 5e
.. can two gnolls make baby gnolls the usual way humanoids reproduce? Or some other way?
The two forms of reproduction could potentially co-exist; a precedent for this is how Corellon Larethian, being the original creator of elves in the Forgotten Realms, doesn't prevent elves in that setting from making little elves as well in the usual manner (@GMJoe, thanks). This relationship, in 5e, is carried over as shown in Mordenkainen's Tome of Foes on page 35. With the idea of some carryover, there is some mild support for this theme as regards gnolls in the entry for Yeenoghu:
During his rampage across the world eons ago, the race of gnolls
sprang up in his wake (MToF, page 29).
It's not a detailed treatment, and is open to interpretation, but one could infer from that a case of "Yeenoghu created them, and then they went forth, were bloody handed, and multiplied" when we tie it to previous edition lore.
1 In 1e 'humanoid' applied to orcs, bugbears, gnolls, goblins, etc and 'demi human' applied to halflings, elves, gnomes, dwarves, etc).
2Giant class creatured, per PHB p. 24 (Ranger description) were bugbears, ettins, giants, gnolls, goblins, hobgoblins, kobolds, ogres, ogre magi, orcs and trolls. The ranger had bonus to damage against these kinds of creatures, an early version of 'favored enemy' of 5th edition).