Your fingers will stop hurting from playing guitar once they have toughened up enough to deal with the tension of your guitar strings. If you play nylon string acoustic or electric guitars, this may only take a few weeks. If you play a steel-string acoustic guitar, it may take a month or longer.
In respect to this, are my fingers to fat for guitar?
One may also ask, can your fingers bleed from playing guitar? The Presence Of Friction
This is also since the guitar strings are made of metal which is hard and thin. Constantly pressing down on them can result in the top most layer of the fingertips experiencing a tear. As the dermal layer below becomes exposed, the fingers start to bleed.
Beside this, how do I make my guitar strings less painful?
Ideally, you want to get the string as close to the frets as possible without hearing any string buzz when playing. Lowering the string action will alow you to exert less force to press the string down, thus less finger pain! (More about string action).