An electric current has a magnetic effect. You can show this by passing a wire through a piece of card and placing plotting compasses on the card around the wire. With no current the needles all point the same way, towards the Earth's north. Switch the current on and the needles turn to line up with the new field. Switch it off and they return to pointing north.
The magnetic field around a straight wire forms concentric circles around the wire, in a plane at right angles to it. Move the compasses around the wire and the needles always point along the circle, so the field has no start or end point.
The direction of the field depends on the direction of the current. If you reverse the current, the compass needles turn through 180 degrees and the field direction is reversed. To find the direction, use the right-hand grip rule: point your right thumb in the direction of the current and your curled fingers show the direction of the field.