Let's say 6V, 4Ah. Do I need to do anything so that the arduino is not fed to much power or so?
Actually, you'd like to have a bit more voltage.
The actual current "drawn" by the Arduino depends on the Arduno and what's plugged-into it. The amperage (or wattage or volt-amps) for a battery or power supply is the maximum it can supply. For example, if you connect the Arduino to a 12V / 500 Amp car battery, it will still use only a few milliamps. Typically the voltage is (relatively) constant, and the current depends on the load. ([u]Ohm's Law[/u].*)
Or if you touch the terminals on your car battery, you won't even feel it, because 12V can only "push" a few microamps through the megohm resistance of your body. (You can get a dangerous shock while connecting/disconnecting a car battery because the coils can generate lots of voltage.)
The [u]specifications[/u] say that the Arduino can run from a 5V regulated source, or from an unregulated source of 6-20V, with a recommended minimum of 7V. The regulator needs some "extra" voltage to work, so you could have problems as your 6V battery starts to discharge and falls below 6V. You can run it from 5V, or from 6-20V, but you should not run it between 5V and 6V.
- We don't actually know the impedance/resistance (Ohms) of the Arduino, and it varies depending on conditions. But if we measure the voltage & current, we could calculate the effective impedance, if for some reason we wanted to. The important thing is to understand the relationship between Volts, Ohms, and Amps... If you want to increase current (Amps), you usually need to increase the voltage, or lower the resistance.