Theres two different approaches, passive and active stability on all three axis.
X axis (roll):
In the X axis, flying wings are stabilized the same as any other plane.
Passive stability is achieved through a slight upwards dihedral between left and right wing. As such the "lower" wing creates slightly more lift in upwards direction and allows the plane to roll back to horizontal flight.
Active stability is achieved through ailerons near the wing tips which create a controlled differential lift allowing the pilot or flight computer to control the roll velocity.
Y axis (pitch)
Passive stability in the Y axis in traditional planes is achieved through the high-leverage corrective force of the horizontal stabilizer (with the exception of canard type planes where the main wing itself takes this role)
Active stability is achieved through elevator controls on this stabilizer, which increase or decrease the vertical force in one or the other direction.
In a flying wing this stabilizer is not present. Instead the rearward area of the main wing takes this role. For this to work, a stable flying wing needs to have wings that are significantly swept backwards in such a way that the overall torque force at both positive and negative high angle of attack is always decreasing this angle of attack.
Active stability is achieved through control surfaces at the very back of the wing. These are often the same control surfaces also used for Roll control, but deflecting in unison instead of opposite directions (Elevons)
Z Axis (yaw)
Similar to pitch, the passive and active yaw control on conventional planes is done with a stabilizer fin with a rudder at the tail.
In true flying wings this is not present (Some don't even have winglets) But the high wing sweep (usually the wings of a flying wings meet at roughly 90° angle at the tip) causes a higher drag force at the forward facing wing if the craft yaws to one side, which enacts the required corrective force.
Active control is achieved by causing additional drag through some sort of braking flaps near the wing tips (the actual implementations vary - split elevons - separate break flaps - ...) This can also be augmented by using differential thrust.
(Note: The corrective force is much lower than that caused by a tail fin. As such a powered flying wing should have its engines relatively close to the center, otherwise a one-engine-out scenario would cause an uncorrectable yawing moment. This however limits the effectiveness of differential thrust if the craft is supposed to stay flyable in such a condition)
Speed and stall stability:
A speed stable plane has its nose pitch up at higher speeds and pitch down if the craft gets slower, thanks to the center of gravity being in front of the center of lift, which causes the nose to drop. This is balanced out by a (usually parasitic) downward force from the horizontal stabilizer acting at the tail of the plane. This arrangement of forces should also cause the nose to drop and the angle of attack to reduce in a stall situation.
As a flying wing does not have this stabilizer, a similar balance of forces needs to be achieved through a careful design of wing profile and twist.
If you look at Horton flying wing glider designs for example, they have a "thick" profile creating the majority of lift in the center (which thanks to the wing sweep is also the front) Towards the end and back of the wings, the profile becomes thinner and more symmetric. At the same time, the wings are slightly twisted, so the intrinsic angle of attack is a few degree lower at the tip (and as such at the rear of the wing) than near the nose.
At high speeds, the front of the wing creates more lift than the back and rises the nose. This part has the highest wing load and will stall first, while the swept back outer wing area - thanks to its profile, lower AoA and lower load will not have stalled yet. The nose drops, and the control surfaces in this rearward part stay functional.
It should be noted that not all flying wing designs did achieve a safe stall behavior. Some, like early 1940's and 1950's American designs failed to implement stall stability correctly, while others (like the B2 bomber) the plane was deliberately designed aerodynamically unsafe to faciliate other features (stealth) which would have been compromised by a "twisted" wing.