Don't worry about the actual current flow, (which is electrons going from negative to positive). Think of every electrical user as a simple circuit consisting of a battery, two wires and the electrical device: (conventional) current flows from the positive terminal of the battery, through the wire to the device, then from the device to the negative terminal of the battery completing a circuit. In actual fact, there will be switches and fuses or circuit breakers between the battery positive and the user, allowing control and protection of each user.
A negative earth system simply means that instead of there being a return wire from the device to the negative terminal of the battery, the aircraft (or car's) metal chassis is used as that return wire. This reduces weight and complexity. Each user therefore has a positive connection from a cable, but its negative connects to the chassis somewhere nearby. The negative terminal of the battery is also connected to the chassis, so the returning current from all users can return to the battery.
An alternator usually has 3 coils, and each coil produces a sinusoidally varying voltage: starting at zero, increasing to a max positive voltage, then reducing to zero, before increasing to a max negative voltage and back to zero again. This is one cycle. The cycles from all three coils drawn on a graph of voltage against rotational angle will overlap, 120 degrees apart. This is effectively 3 phase. However, each coil is fed through diodes which switch its output onto the positive or negative terminals of the alternator as its output changes polarity. The alternator must always be connected across a battery, so the result is a fixed DC voltage with a ripple voltage superimposed on it. (This ripple DC can sometimes be heard on the intercom or radio as a tone varying with engine speed)
Users such as motors and heaters are fine with ripple DC, but others, such as radios and navigation equipment require even smoother DC, so have smoothing circuits built inside them. These vary in complexity according to the equipment's requirments, but a capacitor connected across the positive and negative will have a smoothing function. It would need to be 250 microfarads or greater to have a useful effect. Resistors will not smooth ripple DC at all, but chokes, and more complicated voltage regulators will.
Hope this helps.
Last edited by Uplinker; 22nd May 2012 at 22:09.