Using ADC with barebones Arduino

A simple low pass filter would be a 10 ohm resistor and a 220uF electrolytic + 10uF ceramic - this reduces all noise from 100Hz up, and in particular will kill off a lot of the digital noise (which is mainly high frequency). There will be a little voltage drop through the 10 ohm resistor but probably only a few millivolts.

Alternatively an RFC can be used (radio-frequency choke) instead of the 10 ohm resistor. Choosing the right RFC is more involved though.

If you are running from a battery you'll find there isn't that much noise on the 5V rail from just the microcontroller. Running from a switch-mode power supply or DC-DC converter and you'll see definite noise if you don't filter it out in my experience.