This is covered in Star Wars Tales #10. Maul is off killing Jedi survivors when he comes across a weapons master who bests him with a simple wooden staff. Recognising that he needs an "edge", he comes up with his funky two-bladed lightsaber.



The process of making his lightsaber is also described in Darth Maul: Shadow Hunter.
The intensity of his connection to the Force brought back a memory:
another day of intense focus of his power. The day he had constructed
his lightsaber. Maul was not wont to revisit his past, unless doing so
somehow served his master, but the satisfaction of the creation, the
perfection of focus, and the highly charged connection to the Force
that had wrought his weapon stood out now in his memory.
The specialized furnace, which he had created from plans taken from
his master’s Sith Holocron, had radiated an intense heat as it shaped
the synthetic crystals needed for his lightsaber. But rather than
leaving the kiln chamber and allowing them to form on their own, he
had remained near the device, concentrating on the metamorphosing
gems, using the Force to purify and refine the lattice of the
molecular matrices.
Most Jedi used natural crystals in their lightsabers; Adegan crystals
were the gems of choice. Most of the other components of a lightsaber
were easily obtained—power cells, field energizers, stabilizing rings,
flux apertures—but not the crystals themselves. They had to be mined
in the Adega system, deep within the Outer Rim Territories. The
difficulty of using natural materials meant that the alignment process
could take a long time—and the calibration had to be perfect, because
mismatched crystals could destroy not only the lightsaber, but its
creator.
Finding and aligning the crystals was a Jedi test, but it was not the
way of the Sith. The dark masters of the Force preferred to create
their own synthetic crystals, to match the harmonics in the searing
heat of a crucible and thus take their creation of the weapon to a
deeper level.
Maul had sat by the furnace, focusing his hatred of the Jedi to a
fiery peak and expanding his control of the Force, which he used to
manipulate the molecular structures of the four gems required for his
double-bladed weapon. The choice to make two blades instead of one had
been an easy one. Only an expert would even think of trying to handle
a double-bladed weapon, and he would be no less than an expert. The
glory of the Sith required it, as did his master.
Not even the compressed ferrocrete walls of the pressurized chamber
could entirely contain the intense temperature required to form the
crystals. Hour after hour had passed, the searing heat washing over
the apprentice. But his control had not wavered; the pain had not
swayed his focus. Layer after countless layer of the crystals had been
laid down, aligned, and perfected. It had taken days, days without
food or water or sleep, but eventually he had sensed their readiness.
Then he had deactivated the furnace and cracked it open. There,
sitting in the formation crucibles, had been his four perfect
crystals.