Separate power for the Arduino is the only properly safe way. 3 small servos means maybe upto 3A is
required from the supply, 1A is inadequate (its barely adequate for one small servo).
If you do share power you need to ensure the Arduino get a stable 5V without spikes and drop-outs,
which might mean adding LC filtering, or a DC-DC converter to isolate from the motor-induced noise
on the servo supply.
Capacitor would need to be large, 47,000uF and up to have much effect on drop-outs I fear, but it does reduce
spikes substatially so is worth doing, even as low as 1,000uF.
You should have separate leads from the supply to servos and to Arduino, put capacitor at the Arduino.
That reduces IR voltages on the motor supply and ground wires from hitting the Arduino, but can't eliminate
overloading of the supply.
Obviously you would select a capacitor with a large enough working voltage.
A large capacitor is making up for an inadequate supply, ie covering short drop-outs. With a
supply capable of providing enough current the capacitor only has to quell the spikes and noise
and can be smaller.
There's a clever extra trick, add a diode (preferrably schottky) between the supply and the Arduino
5V pin and its capacitor. Then any dropouts aftect only the servos and the capacitor only has to
power the Arduino, stopping it reseting.
However a servo can easily misbehave during a voltage drop-out, since its internal controller
will also reset or get confused.
You want a 5v line from the charger to go to the servos. Basically cut off some of the insulation, find the usually red wire, strip that insulation, and make a lead off it for your servos without cutting it.