The purpose of rosin is to aid the bow in grabbing the strings. You want enough rosin to do this, but not so much that the excess creates a coating on the instrument or bow. Violin, Viola and Cello rosins are very similar; Bass rosin is notable for being much softer – the better to help the bow grab the thicker strings. There are many varieties of rosins available; lighter rosins will typically grab less than darker rosins. When heat and/or humidity is high you may want to use a lighter rosin; when it is cold or dry, use a darker rosin.
“Un-mounted” rosins should be rotated to maintain a flat surface; deeply grooved rosin can damage the sides of the bow.
You should rosin as often as you need to, which can mean a couple times a day or every couple of days depending on your duration of playing, the type of rosin you’re using and the surrounding weather conditions. This is something musicians develop a feel and preference for over time. In the early stages, consult your teacher for guidance.
For Violins, Violas and Cellos, you apply rosin in long, slow strokes back and forth along the full length of the bow (hair that needs more rosin will grab it and hair that is sufficiently rosined will slide over it). For Basses, the technique is fast strokes from frog to tip — one way only (the rosin is too soft to use a back and forth stroke).