Hi Englishman
This is a subject that I've looked into too. I hope I haven't got the wrong end of the stick, but I think you are asking what the bible says about the issue. If I'm wrong, please ignore the rest of this post :-(
From the point of view of mainstream Christianity (Protestants, Baptists, whatever) the whole 'anointed' experience is your bog standard Christian experience. How does the affected person know about it? It's undeniable. God breaks into your life and shakes it up. It happens in a different way for everyone, but it has the same effect.
The JW's don't want anyone to catch on to the fact that it's freely available to everyone who seeks it. They used to teach that it was only available to 144,000, who would all be JW's - obviously. Then the society grew beyond 144,000. Oops! But what do you know, at just the right time God gave them new light. Allegedly, there was *another* set of (2nd class) Christians, who would obey these 144,000. Phew, panic over.
As Amazing says, if you look at the scriptures, the Greek behind them, etc you find that the great crowd and the 144,000 are all in the same place - the kingdom of God - variously called heaven, Jerusalem, Mount Zion etc. They live happily ever after with Jesus. From a Christian's point of view, that's all that they need to know. They will be with Jesus forever, so they don't care where they are and what they've got to do all day. Heck, Man U could win the cup for the rest of eternity and it just wouldn't bother them :-).
What happens to them whilst they are still here? They receive the gift of the holy spirit - i.e. they are inextricably linked to God and develop a father:child relationship with him. The spirit helps them to understand the bible, what God's will is and begins to change them from the inside. They gradually become more Christlike as they get to know him better. But they still have their own will, so often still go their own way and ignore what the spirit is saying (i.e. sin). That's why they can seem like hypocrits (sp?). But God loves them anyway, 'cos he wants children not robots. (i.e. doctrine of salvation by faith vs the JW's doctrine of salvation by obeying the borg).
If you want to look up the theology, it's all in the justified/sanctified/glorified section (the 3 stages of being saved from the 1st moment of believing to the arriving in heaven bit).
To explain the 144,000 thing. Revelation is fond of numbers, especially 7 (signifies perfection and hence the imperfection of the beast - 666) and 12 (disciples, tribes, thrones, gates to Jerusalem, etc). 12,000 from each of the 12 tribes is 144,000. It's a symbolic thing.
Englishwoman
xxx