describe several ways in which you could, even briefly, experience weightless.

Weight of the free falling object is equal to the mass (m) of the object times the free-fall acceleration (g) on that surface.
So, W = mg
The weight of the body would be zero where, there is no gravity (g=0) and the effect will be achieved only in deep space, far from any star or planet.
In a spacecraft drifting with its engines off, the astronauts would float freely. If the engines fire, the resulting acceleration would cause the ship to be noninertial frame; in the astronauts frame of reference, the floor of the accelerating ship would exert an upward force that would be perceived by the astronauts as similar to weight. This effect is called “artificial gravity”. Therefore in artificial satellite you also feel weightlessness.
A body in free fall near the earth’s surface has no floor to push on it and therefore would feel weightless. If you were inside a chamber that is also in free fall, the floor would not push on you and you would feel no sensation of weight.
Also at the center of the earth, the weight of the body becomes zero.