I've done this enough that I'm now ambidextrous with it. I can use one hand to alternately block a nostril and clear the other, without making a mess of myself.
The easiest way I've found for starting out is the cross-over. Left index finger used to press/block right nostril while tilting head toward the right (aiming nostril toward left), keep your left elbow in and fire away. Reverse for opposite side.