This a good video on how to do this:
How To Start Calisthenics - PULL UPS | THENX
Some of the recommendations on how to achieve one pull-up can be a bit detailed for my taste. They involve different grips, negatives etc.
I do not doubt it is effective, but it is also a lot of work and tedious.
Here is more or less how I achieved one pull-up (with some improvements in hindsight):
Start by doing Australian pull-ups (inverted rows): https://www.youtube.com/watch?v=sJe5xLbxaxg
Say you manage to do 3 of these. Then pause for 3 minutes and do 3 more.
Repeat until you have done 10-15 in total.
2 or 3 days later you repeat this workout.
When you can do 8-10 Australian pull-ups in a row; move on to warming up with Australian pull-ups and then do chin-ups.
When you can do 3 chin-ups in row; you should be able to do 1 pull-up.
Lack of volume is a practical problem when it comes to strength training. It means that you are probably better off sticking to chin-ups until you can do 3 pull-ups.
Regardless of how strong you become it is always good to do a combination of Australian and ordinary pull-ups.
That is because Australian pull-ups are better for posture, whereas pull-ups are more useful (functional).
Also remember to eat enough protein and also some carbs and fat.
It is better to gain a little bit of extra fat when gaining muscle.
This fat will be easy to loose again later, since your slightly larger muscles will consume more energy.
while doing one pull-up is a great goal, I also think you should train the rest of the body.
I recommend you check out the Starting Strength program.
Alternatively you could also do push-ups + squats.