When my mum got a new kitten she didn't take any special measures to introduce her to our 14 year old male cat. He was a bit affronted at first, having been the apple of everyones eye on his own for 11 years but he soon got over it and and having the kitten seemed to breath new life into him. (Although at 4 I'm sure thats not a problem for your cat!)
My mum made sure, while the kitten was still young, that she never left it alone with our cat, although supervised she allowed them to mingle (the kitten fell inlove with the cat immediately, though the cat has never been quite as keen). Although I suppose it depends on the cat, our cat is very gentle and placid and never really lashes out.
At night or if my mum was out she shut the kitten in the living room with a litter tray so that the cat could still come and go as he pleased.
As for intoducing the kitten to her surroundings, I wouldn't worry too much about it, at that age they're still so tiny and get tired quickly, leave her to explore as she wishes.