to improve your chinups from one grease the groove. Every time you pass the chunup-bar do a chinup your central nervous system gets used to it then your muscles will get stronger and you will start to improve your numbers.
I used to only be able to do 4 (only 1 from dead hang) and I increased that number to ten in 4 weeks by doing dumbbell curls and practicing chin ups. Once you can do enough chin ups to make a workout out of it, then you'll start being able to do more and more. This is from experience and should work for you too.
Once you get going I've found a really quick way of increasing the reps.
Take a starting point of 3sets of x reps, but work it so the final set you try to max out, but with a target of x. (x/x/Max).
To begin with, you may only be able to do 3 sets of x. But the moment the final set exceeds the target (x), any extra get loaded evenly over to the front sets of the next time you do your pull ups for your new target.
To illustrate, I've only recently started doing pull ups again (wide arm overhand) when I go for a run: stopping at a kids playpark and doing it on the swings. Here's how I've progressed so far.
Session.....Target.....Actual.....Difference/Extra reps next sesh
1................5/5/5......5/5/6.........+1
2................6/5/5......6/5/6.........+1
3................6/6/5......6/6/7.........+2
4................7/6/6......7/6/6.........0
5................7/6/6......7/6/7.........+1
6................7/7/6......7/7/8.........+2
So next session I'll be aiming for 8/7/7. Once I can do 10/10/10 I'll introduce a 4th set, target 10/10/10/Max. Again, once Max set exceeds the target (10) I'll start adding the reps in the same way as above.
These 6 sessions have been done over two weeks (I run every day, but do these every other run).
One question on pull-ups though, I pull up so chin goes over the bar. What difference is there between this and pulling up (same grip) so the bar touches the back of your neck?
Depends on what you're training for. I prefer a balance of strength & muscular endurance; for me it's not just about size and absolute strength (I consider myself a fell runner first and foremost-which involves a lot of climbing and running with weight).
This technique would still work for a beginner: get so's you can do 3x5 unweighted, then gradually add weight.