Expressions are capable to animate an object without necessarily make use of keyframes.
One of the most simple expressions, and also one of the most useful, is Wiggle.

To apply an expression, select the proprieties one by one and go to Animation> Add expression. The shortcut is Alt+click on the animation stopwatch.
One the expression have been added, press Enter on the numeric pad or click any area outside the expression, to close the expression editor.
To temporary disable the expression, click the = icon on the left side of the expression.

- To randomly wiggle position use:

wiggle(5,50)

where 5 is frequency (times per second)
and 50 is magnitude (how many pixels movement)

- To randomly wiggle rotation:

wiggle(5,50)

where 5 is frequency (times per second)
and 50 is magnitude (how many degrees movement)

- To randomly wiggle scale:

wiggle(5,50)

where 5 is frequency (times per second)
and 50 is magnitude (how much in percentage)

- To randomly wiggle position and scale, just horizontal movement:

w = wiggle(5,50);
[w[0], value[1]]

where “w” is the short name for wiggle(5,50)
[0] is x, horizontal
[1] is y, vertical
“value” commits the actual value
to start a new row, just press enter on the keyboard

- To randomly wiggle position and scale, just vertical movement:

w = wiggle(5,50);
[value[0], w[1]]

where “w” is the short name for wiggle(5,50)
[0] is x, horizontal
[1] is y, vertical
“value” commits the actual value

- To equally animate scale on both x and y (horizontally and vertically) use the following expression:

w = wiggle(5,50)[0];
[w,w]

Where “w” sets a unique value for wiggle, and the array [w,w] apply the same value to both x and y

The same expression applied to position, makes the layer moving diagonally only.