A wire carrying an electric current is surrounded by a magnetic field. You can show this with plotting compasses. Pass a straight wire vertically through a piece of card and place plotting compasses on the card around it. With no current, every needle points north because of the magnetic field of the Earth. When the current is switched on, each needle turns away from north and lines up with the field made by the wire.
The field lines around a straight wire are circles centred on the wire, in planes at right angles to the wire. The plotting compasses on opposite sides of the wire point in different directions, following the circle. If the compasses point clockwise round the wire, then reversing the current makes them point anticlockwise. Reversing the current reverses the direction of the field.
You can find the direction using the right-hand grip rule. Point your right thumb along the current and your curled fingers show the direction of the field.