Monalua,
If you have a cradle, just drop your new battery in the rear slot overnight. That way you can still carry your Ax around with you...
If not, then swap the new battery for the old and plug your sync-charge cable in (Axim turned off) for about 8 hours or so. Remember, you can't overchrage the battery.
You may see some increase in battery run-time after a few charge-discharge cycles.
And yes, carry the old battery around if you can - if not, one day you'll wish you had
But remember, even if you don't use it, the spare will gradually loose charge. I rotate by batteries at least once a week whether I need to or not, just to make sure I have plenty of juice.