I want to achieve a effect where a black image that covers the whole screen slowly fade away, revealing what's behind it, by decreasing its alpha value in its fragment shader.

The way I do it is create a quad that covers the whole screen. Its texture is a complete black image. I declared a variable a whose value is 1.0, and a uniform dt for which i will send the delta_time, the difference between the last frame and the current frame, each frame. And then I subtracted dt from a, and used a as the alpha value for the final color's alpha value. But it seems that the result is the image is still completely black. I guessed the variable a is still 1.0. I'd like to ask if there's a proper way to fade away the black image?

a will be set to 1.0 every time the fragment shader is called, so it won't gradually decrease as you decrement it by dt.

Try calculating the alpha inside your normal application and send that to your shader instead.

I have tried sending a -= delta_time for that from the main application, but it seems that no matter how large a value i give it it always decreased too quickly, like a -= delta_time * 0.00001f. a is 1.0f.

    uniform float alpha; //This needs to come from the main application
    in vec2 textuv;
    uniform sampler2D textsampler;
    out vec4  color; float a = 1.0;
    void main()
    {
       color = vec4 ( texture2D(textsampler, textuv).rgb, alpha );
    }

I have tried sending a -= delta_time for that from the main application, but it seems that no matter how large a value i give it it always decreased too quickly, like a -= delta_time * 0.00001f. a is 1.0f.

You'll need to adjust your equations from your main application.

When you want the effect to start, set 'a' to 1.0f.

a = 1.0f;

Every tick, you do:

a -= (deltaTime / DurationOfEffectInSeconds); //'DurationOfEffectInSeconds' is a constant-like variable.
if(a < 0.0f) a = 0.0f;

This uses math to get the exact result you want.
If you want it to last five seconds, set 'DurationOfEffectInSeconds' to 5.0f. If you want it to last half a second, set it to '0.5f'.

Another way to do it is by having a timer and subtracting time from it. You then calculate the alpha by how much time is remaining.

When the effect begins, you do:

fadeTimeRemaining = DurationOfEffectInSeconds;

Every tick, you do:

fadeTimeRemaining -= deltaTime;
if(fadeTimeRemaining < 0.0f) fadeTimeRemaining = 0.0f;

To calculate the alpha you do:

float alpha = (fadeTimeRemaining / DurationOfEffectInSeconds);

And then you pass that to your shader.