One way to look at the situation is to note that velocity change is the result of an acceleration applied over some period of time. In the case of a wheel in a precessing mode due to wheel rotation and external torque, the velocity change component perpendicular to the plane of rotation of a point on the wheel lags the change in acceleration component perpendicular to the plane of rotation by about 90° as the wheel rotates and precesses.
The end result is that the reaction of a spinning wheel to an external torque will be a precession about 90° "after" the torque. This effect applies to a single rotor helicopter, so the "cylic", which controls roll and pitch rotation, is advanced by 90° from the pilot input to compensate, and the helicopers roll and pitch responses are precession like reactions to torque inputs from the rotor blades.
The reason while the wheel doesn't fall down is that the torque due to gravity and the line holding the wheel up is opposed by an equal and opposing torque if the wheel is precessing at a constant and "proper" rate. The other situation is that the free axis end of the wheel will oscillate up and down as the rate of precession increases and decreases.
The other interesting bit here is that the center of mass of the wheel will tend to stay on the same horizontal plane moving the free axis up or down depending on the movement of the supporting line and how far off from vertical the supporting line is at any moment (the ideal situaion would be a massless supporting line). Look at video #9 on this web page for an example of this:
http://www.gyroscopes.org/1974lecture.asp
Video #18 on that same web page has small masses located at the ends of the spokes that demonstrate the explanation I gave above, but in the video the effect is noted but not explained.
how does angular momentum create a perpendicular force?
It doesn't create a force, the precession creates a torque that opposes the torque due to the supporting line and gravitly, so that the wheel doesn't rotate "downwards", and the vertical component of tension in the line is what opposes gravity.