There are several methods of adding new keys. Namely:
In the 3D Viewport, pressing I will bring up a menu to choose what to add a keyframe to.
Hovering over a property and pressing I or with the context menu by RMB a property and choose Insert Keyframe from the menu.
There are several methods of removing keyframes:
In the 3D Viewport press Alt-I to remove keys from selected objects on the current frame.
When the mouse is over a value, press Alt-I.
RMB a value and choose Delete Keyframe from the menu.
Removes all keyframes from the selected object.
This example shows you how to animate a cube's location, rotation, and scale.
First, in the Timeline, or other animation editors, set the frame to 1.
With the Cube selected in Object Mode, press I in the 3D Viewport.
From the Insert Keyframe Menu select LocRotScale. This will record the location, rotation, and scale, for the Cube on frame 1.
Set the frame to 100.
Use Move G, Rotate R, Scale S, to transform the cube.
Press I in the 3D Viewport. From the Insert Keyframe Menu, select LocRotScale.
To test the animation, press Spacebar to play.