So like my title suggests. I am not sure how to read a book.

..."haha illiterate"...

Of course i mean in the game. Im the DM and one of my players expressed the whish to find and possibly buy a book to read it and learn
about magic (hes a sorcerer and hasnt had any formal training like a wizzard and would like to learn more).
So of course i found the downtime activity which takes him a week and blablabla so on and so forth...

But i was wondering how i should handle it, or if there is any ruling for it, when my player buys a book and reads it for example at the campfire or something like that.

Sorry if i missed a point in the PHB or DMG that mentioned this. And thx for your help in advance :)

I do not know the rules per se on this but I would think most reading would be done for flavor/RP.  If one could just read during all down time and improve skills or increase spell base or such, everyone would do it.  I would think for reading to have a beneficial effect (besides possibly improving roles for arcana or history or such, or on the specific info in the book) it would require a certain intelligence level to "self teach" and much practice time, likely some coin spent buying things needed to practice.  

All in all, I think the DM should decide how likely it is the character can self improve, what limits there are to it so it doesn't imbalance the game, etc...  

There are no rules, it's an RP thing. Maybe over time they gain Arcana proficiency as per the downtime training rules.

Beyond that it's RP and whatever you decide as a DM.

Thank you for your fast responses!

And thats exactly whats going to happen @Cyb3rM1nd. What i did previously was maybe a lil dick'ish... i said he only has half proficiency in arcana since he didnt say anything about actually learning what schools of magic there are. So now when he "feels" magic i describe it very vaguely to him (he feels it due to him being a knot in the magic weave as some sorcerers are as far as i understood). And of course he wants to be able to understand it better so he would read a few books and improove his knowledge -> full arcane proficiency.

A Long Rest is 8 hours, but a non-elf only needs to sleep for 6 hours/LR. They could also therefore read for an hour or so every long rest.

Quote from IamSposta >>

A Long Rest is 8 hours, but a non-elf only needs to sleep for 6 hours/LR. They could also therefore read for an hour or so every long rest.

 
Actually longer. 2 hours of the long rest can be spent awake and doing light activities like reading.

One presumes about an hour to eat, poop, sharpen weapons, etc.

Some of this would be reflected in feat choices.  For example, if he wants to say his study of magic should allow him to cast spells as rituals, there's a feat for that.  If he has to choose between a CHA bump and a Skilled feat, well, how bad does he want to "know magic?"