How to change a texture's (or a material's ?) opacity ?

The shader is basically a program executed by your graphic card that will compute the color of each pixel of an object.

The shader will take input (texture, values, colors, ...) to compute the pixel colors.

So, for transparency, first you need a shader that handles transparency and then you need to set the right input to the shader.

Usually, a shader takes the alpha channel of the main texture (RGBA) to compute the transparence of the pixels, but that can change according to the shader you are using.

The shader inputs are defined in your material and materials are just another name for a shader with specific inputs.

So, for your problem, you probably need a texture with an apha channel set to half-transparency and set it as the main texture of a shader that handles transparency.