There are two classes of symbol motions: those that are equivalent to an addition or subtraction operation, and those that are equivalent to a multiplication or division operation.
In the addition/subtraction class, you start by chunking the expression you want to move. If there is a + or a - to the immediate left of the expression, you include that symbol in the chunk. As you move the chunk, you multiply its contents by -1 (i.e., just flip its sign). You normally insert the contents of the chunk at the far right of the opposite side. You can also insert it in another location, if you add it in between terms that are being added or subtracted together.
For the multiplication/division class, start by chunking the expression you wish to move. If it is in the numerator of its current side, you will move it to the denominator of the other side; if it is on the denominator, you move it to the opposite side's numerator. (If one side does not look like a fraction, it actually is - just put it over 1.)