Quote Originally Posted by G2Ident89 View Post
The one: 'They were going - to give him the book', meaning that they set out 'to give him the book'. In Russian, I think this would be something like, 'они пойтили давать ему книгу' with the intended meaning of something more like, 'They set out to give him the book'.
I don't understand well the sense of this. Does it mean "they started the process of giving him the book?" Sentence looks strange. Though it can be translated as "Они начали давать ему книгу."

The verbs "идти, пойти, ходить etc" normally are applied to the pedestrian motion. Here they are not equivalent of the English "to be going to do smth."

Quote Originally Posted by G2Ident89 View Post
The second: 'They were - going to give him the book', meaning that they intended 'to give him the book' but the action was never actually undertaken. This is where I'm confused. How would you translate this sentence with this second intended meaning into Russian?
'They were going to give him the book'='they intended to give him the book'='Они собирались дать ему книгу.' If you want to say in addition that the action was never actually undertaken, you can add corresponding phrase:
'Они собирались дать ему книгу, но так и не дали.'='They intended to give him the book but never gave.'

Can you just put it in the conditional, so that you have, 'они пойтили бы давать ему книгу'?
I don't see the way to do it without the full context. Please give the full sentence to translate, which contains all the necessary context about the idea.

Quote Originally Posted by G2Ident89 View Post
Also, can you clarify the meaning and use of 'собирались'?
It is past plural third person form of the imperfective verb "собираться" , which means "to intend to", "to prepare to", "to plan to".