Using a foam brush is possibly the best way to apply stain with the most accuracy and least mess. The foam absorbs the stain like a sponge and holds it until it is pressed on the board. This avoids drips and runs, as long as you do not overload the brush. Foam brushes also come in a variety of widths, making it simple to choose one appropriate for the task at hand. (Ref 2 vid clip min 2)
A clean rag is an effective way to apply stain to tongue and groove boards. While it does not always offer the ease that the foam brush does, it is something everyone has on hand. Choose an absorbent cloth so that it acts like a sponge and soaks up the stain for application. Absorbent cloths, like terry, microfiber or dish washing rags, reduce mess while applying the stain. Also use a cloth so you do not plan to reuse, as the stain permanently stains the rags.
Stain may also be painted onto the boards. Since a paint brush is not as absorbent, drips are a problem. Avoid them by not loading too much stain onto the brush at one time. A paint brush used for stain can be cleaned with mineral spirits and used again and again. Angled paint brushes may also be better suited for getting into tight corners, simplifying your stain application.
Some people prefer the hands-on approach to staining. Wearing vinyl or latex gloves is recommended if you do not want your hands to match your tongue and groove wood. Simply dip your fingers into the stain and smear it onto the wood surface. You may also wear a cloth glove over your disposables for some absorbency. Absorbency in the applicator, whatever it may be, increases the smoothness with which your stain goes on. (Ref 3 section Stain)