Simple "Path" Animation

Start Blender.
Add new "Curve" by using "Shift" + "a" key

Go to wire-frame view mode
(So that you can see the added curve clearly.

Select the "Curve" by right clicking.
Go to edit mode using "TAB" keu.
Adjust the curve points & handles using right click to select
and "g" key to move it around.

Choose the object to animate using right click.
Go to object constraint panel.
Add constraint & choose "Follow Path"

Choose target as your curve & enable "Follow Curve"

Go to start frame (eg: frame 1).
Select the curve.
Go to "Object Data" panel
Move mouse over evaluation time.
Press "i" key to insert frame.

Go to end frame (eg: 250)
Key in the end Frames (eg: 250)
Key in "Evaluation Time" (eg: 250)
Move mouse over "Evaluation Time".
Insert the key frame again using "i" key.
Done! Press "alt" + "a" to preview animation.