how do the wise become wise

[Hama]

Well, The Wise, in the context of LOTR are all immortal. So they've had plenty of tuime to accumulate the knowledge and skills to make themselves wise: being superbeings, eg Wizards and Elves also helps, them being probably rather cleverer than the average Human. Not having to worry about imminent death through old age also perhaps helps: can take the long view and study things in more depth.

I think that in general, wisdom/cleverness/intelligence all revolve around being able to make connections in your mind between the different things you have learnt or seen