What special handling characteristics or techniques do biplanes have?
Short answer:

For clarification: Equivalence between biplane and monoplane means than both have the same wing area and the same engine. Then the main differences in maneuvering are:


The biplane has better roll acceleration than an equivalent monoplane.
The biplane has a higher roll rate than an equivalent monoplane at the same speeds.
All biplane flying takes place at lower speeds, resulting in a lower space requirement for all maneuvers. This also means that inertial effects are less pronounced: When pulling up, there is less kinetic energy available for climbing, so (for example) hammerhead turns will end with less altitude gain.


Differences in handling: The biplane has


lower aileron forces for the same roll rate at the same speed
lighter control forces overall due to lower flight speed


Differences in performance:


shorter take-off and landing distances
a lower stall speed
a much lower maximum speed
a lower optimum cruise speed and range
a lower power requirement due to the lower flying speeds, or if both use the same engine, a better power-to-weight ratio


when compared to an equivalent monoplane. These differences are most pronounced if the airplane carries just the pilot and not much payload.

Flying techniques are the same as for monoplanes. Indirectly, differences are likely due to differences in design. Example: Few biplanes profit from having a retractable landing gear while gear retraction makes sense for monoplanes with higher power loading (installed power relative to wing area).

Explanation

Biplanes have two major differences:


Smaller wing span at the same wing area, and
Wire bracing results in very lightweight biplane wings.


The smaller span reduces roll damping and roll inertia, so a biplane will accelerate into a roll more quickly than an equivalent monoplane and will reach a higher roll rate. This is the main difference in maneuvering.

The smaller wing span results in more induced drag if both have the same mass and the same speed. With wire bracing, this condition is unrealistic, and an equivalent biplane will be much lighter. If the structure is a substantial part of the aircraft's mass (this is typical for aerobatic airplanes), the result can easily be less induced drag, despite the lower span, and also lower wing loading. This in turn means that both fly at different speeds: The biplane will be able to fly much slower, but the aerodynamic drag of the bracing will restrict it to low speeds. This also means inertial effects are less pronounced: The lower mass and lower speed of the biplane combine for a marked difference to the equivalent monoplane.

For aerobatic displays this is ideal: All action takes place close to the audience, and the biplane will need a much smaller area for all maneuvers than an equivalent, but heavier monoplane. The downside are low maximum speed and low range.

Another difference in performance are much shorter take-off and landing distances due to the lower wing loading, which results in a lower stall speed. The optimum endurance and optimum range speeds are lower than those of an equivalent monoplane as well, so all biplane flying happens at lower speeds, which is beneficial for training aircraft.

Since control forces are proportional to dynamic pressure, a biplane will have lower control forces than an equivalent monoplane. Here equivalence also means that the relative chord of all control surfaces is the same. In reality, a good designer will select a higher relative chord for the biplane's control surfaces to ensure that control forces are above their required minimum.

The heavy, unreliable engines of the early years made biplanes the ideal way of taking to the air. Once engines became more powerful and allowed higher payloads, the monoplane became better suited to carrying passengers and freight at higher speeds and over longer distances.