Yep, turn the switch on, and the LED should be blinking.
Also, it won't blink if the batteries are almost dead.
Steady means it is paired with your Mac (connected)
But, ultimately, the mouse is only working if you can move the cursor.
The "pairing mode" lasts only 30 seconds or so, that's why I turn the mouse off, so I'm sure the pairing mode comes on.
Turn on the power, put mouse down. Click a couple of times, and that should do it. Try to move the cursor on the screen.
If it doesn't seem to work, try the same process again, until it works (or you give up) If you CAN'T get the pairing to work, open your bottom drawer, and pull out your spare USB mouse - that one that you stuck away because you bought the wireless mouse. Guess what? now you need the USB mouse.
Finally - are you sure the magic mouse is good? This is the step where you change the batteries
Does the light come on at all?
Leave the battery cover OFF - the batteries will stay in place for this test. Some folks report a better connection with the bottom cover off. Try it to see if THAT helps.