Object Picking
This is when we want to take a 2D point on screen and create a
ray in your 3D world, one from your near plane to your far plane. This
ray/line segment is used to pick various objects in our world. Either
using the mouse or some other 2d cursor move around the screen using the
controller.
There are various ways of doing this, below I've shown 3
different way of doing it, just so you can see that there's more than one way to
cook an egg ;)

Invert View/Projection Matrix and multiply this by our 2D point

Use the built in Unproject API (which basically does the inverse
and multiplication for us)

Extract the data from the View matrix and project a ray into the
screen.
First I'll give a snippet of the camera where setting up  just
so you can see where using a simple projection and lookat camera  of course the
principles should work with different projection/orthogonal setups.
Snippet  Setting up camera 
//
Setup a basic camera view and projection for testing
float
aspectRatio
= (float)m_device.Viewport.Width
/ m_device.Viewport.Height;
Matrix camView =
Matrix.CreateLookAt(new Vector3(0,5,5),
Vector3.Zero,
Vector3.Up);
float
nearPlaneDist = 1.0f;
float
farPlaneDist = 1000.0f;
Matrix camProj =
Matrix.CreatePerspectiveFieldOfView(MathHelper.ToRadians(45.0f),
aspectRatio,
nearPlaneDist,
farPlaneDist);

First we just use the inverse of our projection matrix 
probably not the best way as where going to a lot of work by finding the inverse
of our projection and view  but it goes to show that the opposite of what our
matrix does can give us what we started with.
Snippet 
//
Pixel Space  ScreenSpace 1 to 1
Vector2
screenSpace;
screenSpace.X = (
( ( 2.0f * mousePos.X ) / screenSize.X )  1 );
screenSpace.Y = (
( ( 2.0f * mousePos.Y ) / screenSize.Y )  1 );
//
Inverse View/Proj Matrix
Matrix invMProj =
Matrix.Invert(camProj);
Matrix invMView =
Matrix.Invert(camView);
//
Near/Far Point
Vector3 nearPos =
new Vector3(screenSpace.X, screenSpace.Y,
0);
Vector3 farPos =
new Vector3(screenSpace.X, screenSpace.Y,
1);
//
Final near and far ray positions
nearPos =
Vector3.Transform(nearPos, invMProj * invMView) * nearPlaneDist;
farPos =
Vector3.Transform(farPos, invMProj * invMView) * farPlaneDist;

A more optimised way is using the build in API one  just to
note, in C++ and DirectX theres a D3DXVec3Unproject(..) as well. MS is
always trying to help us out. The near and far world points should be the
same as what we got above using our own matrix.
Snippet 
//
Alternative Way!
Vector3
nearScreenPoint = new Vector3(mousePos.X,
mousePos.Y, 0);
Vector3
farScreenPoint = new Vector3(mousePos.X, mousePos.Y, 1);
Vector3
nearWorldPoint = m_device.Viewport.Unproject(nearScreenPoint, projection,
view, Matrix.Identity);
Vector3
farWorldPoint = m_device.Viewport.Unproject(farScreenPoint, projection,
view, Matrix.Identity);

Finally  using what our camera actually holds, we can extract a
starting point and a ray direction.
Snippet 
//
Another way again
Vector3 v;
v.X = ( ( ( 2.0f
* mousePos.X ) / screenSize.X )  1 ) / camProj.M11;
v.Y = ( ( ( 2.0f
* mousePos.Y ) / screenSize.Y )  1 ) / camProj.M22;
v.Z = 1.0f;
Matrix m =
Matrix.Invert(camView);
Vector3 rayOrigin
= new Vector3(m.M41, m.M42, m.M43);
m.M41 = m.M42 =
m.M43 = 0.0f;
Vector3 rayDir
= Vector3.Transform(v, m);
//
We have a ray origin and ray dir  but we can create a near and far
//
as we have with the others as:
Vector3 nearPos =
rayOrigin;
Vector3 farPos =
rayOrigin  Vector3.Normalize(rayDir)*1000.0f;

