While the right hand rule for a straight wire is the one described by another educator, the right hand rule for a LOOP of wire is similar, but notably different.
With your right hand, make a "thumb's up" gesture. The direction your fingers curl is the direction of the current flow around the loop. If you are looking at the loop below with current traveling in the counter-clockwise direction, your right thumb should be facing up or "out of the screen"
The magnetic field will be out of the screen. Likewise, if the current is going the other direction, you orient the curl of your fingers to follow the current and your thumb will be pointing down or "into the screen"
The reason this works: Imagine grabbing the right side of the loop picture above with your right hand so that your thumb points up (the direction of the current. If you look at your finger tips (curled around the wire), they are pointing up at you. As you rotate your and around the loop, keeping the thumb in the same direction as the current, you will notice that your fingers will always point upward.