Rosin is the least glamorous object in the case and the one most likely to be the actual problem. Without it the hair slides over the string and produces almost nothing; with too much it grabs unevenly and everything scratches. There is a correct amount and it is smaller than most beginners think.
What rosin does
It gives the hair grip. A bow works by catching the string, dragging it slightly, releasing it, and catching again — hundreds of times a second. That whole cycle depends on friction, and rosin is the friction. A bow with none simply cannot start the string moving, which is why a brand-new bow appears broken until it is rosined.
How much
A few strokes along the length of the hair, evenly, then play. If a visible cloud of dust rises when you play, there is too much. If the sound is thin and whistly and the bow feels like it is skating, there is too little. Once the bow is working, a few strokes every couple of playing sessions keeps it there — daily rosining is a common and easily fixed mistake.
Tension and the hair
Tighten before playing, loosen after — every time. Hair left tight overnight stretches and eventually warps the stick, which is expensive. Tightened correctly, the gap at the middle of the bow is roughly a pencil's width; more than that and the stick has lost its curve, which is a rehair or a repair rather than an adjustment.
Never touch the hair with your fingers. Skin oil kills grip in exactly the places you touched, and the fix is a rehair. Wipe rosin dust off the instrument and off the stick after playing, with a dry cloth and nothing else.
When to rehair
When hairs have broken unevenly, when the bow will not grip however much rosin goes on, or roughly once a year for someone playing daily. It is routine maintenance rather than a repair, and a bow that has been rehaired feels like a new one — which is worth remembering before concluding the problem is your bowing.