how is electricity produced in a 'battery' and 'dynamo'? (a couple of sentences for each please)
A battery is made from cells connected in series. Each cell has a small voltage and a battery adds these voltages.
Electricity is produced in an electrochemical cell by chemical reactions that remove electrons from the +ve connection or cathode, and transfer electrons to the -ve anode. If the anode and cathode are connected via a lamp, ipod, etc then the cell does work. Be aware that conventional current flow is opposite to direction of electron flow.
A dynamo is a mechanical device that makes a conducting wire move in a magnetic field, or vice versa. When there is relative motion between a conductor and a field a voltage is generated. As above if the wire is connected to an external device work is done.