Q:

OpenGL: Passing random positions to the Vertex Shader

I am starting to learn OpenGL (3.3+), and now I am trying to do an algorithm that draws 10000 points randomly in the screen.
The problem is that I don't know exactly where to do the algorithm. Since they are random, I can't declare them on a VBO (or can I?), so I was thinking in passing a uniform value to the vertex shader with the varying position (I would do a loop changing the uniform value). Then I would do the operation 10000 times. I would also pass a random color value to the shader.
Here is kind of my though:
#version 330 core

uniform vec3 random_position;
uniform vec3 random_color;

out vec3 Color;

void main() {
    gl_Position = random_position;
    Color = random_color;
}

In this way I would do the calculations outside the shaders, and just pass them through the uniforms, but I think a better way would be doing this calculations inside the vertex shader. Would that be right? 

A:

The vertex shader will be called for every vertex you pass to the vertex shader stage. The uniforms are the same for each of these calls. Hence you shouldn't pass the vertices - be they random or not - as uniforms. If you would have global transformations (i.e. a camera rotation, a model matrix, etc.), those would go into the uniforms.
Your vertices should be passed as a vertex buffer object. Just generate them randomly in your host application and draw them. The will be automatically the in variables of your shader.
You can change the array in every iteration, however it might be a good idea to keep the size constant. For this it's sometimes useful to pass a 3D-vector with 4 dimensions, one being 1 if the vertex is used and 0 otherwise. This way you can simply check if a vertex should be drawn or not.
Then just clear the GL_COLOR_BUFFER_BIT and draw the arrays before updating the screen.
In your shader just set gl_Position with your in variables (i.e. the vertices) and pass the color on to the fragment shader - it will not be applied in the vertex shader yet.
In the fragment shader the last set variable will be the color. So just use the variable you passed from the vertex shader and e.g. gl_FragColor.
By the way, if you draw something as GL_POINTS it will result in little squares. There are lots of tricks to make them actually round, the easiest to use is probably to use this simple if in the fragment shader. However you should configure them as Point Sprites (glEnable(GL_POINT_SPRITE)) then.
if(dot(gl_PointCoord - vec2(0.5,0.5), gl_PointCoord - vec2(0.5,0.5)) > 0.25) 
    discard;

I suggest you to read up a little on what the fragment and vertex shader do, what vertices and fragments are and what their respective in/out/uniform variables represent.
Since programs with full vertex buffer objects, shader programs etc. get quite huge, you can also start out with glBegin() and glEnd() to draw vertices directly. However this should only be a very early starting point to understand what you are drawing where and how the different shaders affect it.
The lighthouse3d tutorials (http://www.lighthouse3d.com/tutorials/) usually are a good start, though they might be a bit outdated. Also a good reference is the glsl wiki (http://www.opengl.org/wiki/Vertex_Shader) which is up to date in most cases - but it might be a bit technical.
Whether or not you are working with C++, Java, or other languages - the concepts for OpenGL are usually the same, so almost all tutorials will do well.

