You should not leave the bow hair tightened when the violin is not being played. This places stress on the bow and overtime can cause the bow to warp. It also stretches the hair.
There is a screw on the end of violin bows. This is used to tighten or loosen the bow hair. Turn the screw with your fingers.
Rosin is a processed tree sap (some are synthetic). The rosin makes the hair on the bow sticky and able to grip the strings. Without rosin the bow hair glides across the strings with no sound being produced.
You need to keep the correct amount of rosin on the bow. The correct amount will provide good tone, but not be so much that a lot of dust comes off the hair while playing. Too much rosin also causes the sound to be gritty. Rosin does not need to be applied every time the violin is played. You will eventually get a feel for how much rosin is ideal.
With a new bow, tighten the hair on the bow (just twist the knob on the end). You want enough space to insert your pinky between the bow and hair. Try different tensions to find the idea tone.
Rosin the bow (drag the bow hair across the rosin). At first it takes a lot of rosin If the violin does not make much sound, you need to add more rosin. If needed you can scratch the rosin with a metal object to get the powder started. Low quality rosins are a lot of trouble. It is normally hard to apply and never grips the strings well. Good rosin will make life a lot easier.
The adjustment screw can start to bind. In most cases this can be removed and cleaned.
Humidity can cause problems for bow hair. Too little humidity can shrink the hair and tighten it on the bow. Too much humidity can make the hair lose.
The hair will slowly break and fall out of the bow. This will eventually need to be repaired or the bow replaced. When loss of hair causes the tone to change, or it is lost unevenly and places more tension on one half the bow, it is time to have it fixed.
Some insects like to eat bow hair. This includes moths and mites. Moth balls or similar insect repellent can be used inside the case. Try to avoid contact with the violin itself.
The leather grip on the bow can become worn through. If you notice this, replace the grip area before the wood underneath begins to be damaged.
Whether you replace the hair or just buy a new bow depends on the grade of bow you have. A low grade bow can often be replaced for less than the cost of re-hairing. A good quality bow will be worth the investment of new hair.