Measuring acceleration in g's
If you read the datasheet you can quickly find that the output of the device is 300mV per g.  That means:


Read the analog value
Convert it to millivolts
Divide it by 300


The result is the g value.  If you do it using floating point then yes, you get fractions of a g resolution.

For instance:

float mv = analogRead(0) / 1023.0 * 5000.0; 
float g = mv / 300.0;


If the analog channel has 1024 steps, that's 5/1024 = 0.0048828V per step, or 4.8828mV per step.  Divide that by 300 and you get a resolution of 0.01628g

As for not seeing variations in X when you shake up and down, maybe that is because you really want to look at the Z axis, not the X. X is left/right, Y is forward/backward and Z is up/down.  It's all in the datasheet - it makes for good reading, I suggest you take a look.