You use extraverted Intuiting or Ne when you're brainstorming. When you're projecting ideas into the future. When interpreting alternative meanings and seeing options. When finding commonalities among those options. "We have a pot of rice, what could we do with it? Oh, I know, we could add beans, corn, and cilantro and have a Mexican fiesta! Or, we have brokkoli and thai paste, if we get some coconut milk, we could have a thai curry. That reminds me, when we go to the store, we need to get toothpaste and a screwdriver. I want to get started on that arts project. We can do it together after dinner!"
For people with Ne as their dominant function, they cannot not see -and want to explore- potential possibilities. Virtually anything you say will trigger a whole host of connections between seemingly unrelated items, and the opportunities they hold. Expats preparing for an assignment using Ne are likely to imagine all the possibilities they are going to have in the new country, and what they'll be able to do and accomplish.
If Ne is in different positions in your type dynamics, below is an overview pieced together with only a few items taken from Understanding Yourself and Others, An Introduction to the Personality Type Code, by Linda V. Berens and Dario Nardi. Let me say this again to be very clear: the description of how Ne can be expressed in the different positions is not exhaustive and only meant to give you an overview. I would love to have you comment below how it shows up for you.
If you'd like to practice your Ne skills, take some time to brainstorm up ideas without censoring yourself. Take five pieces of unrelated news headlines and try to find a connection. Play "Six degrees of Kevin Bacon".
Repeat the exercise to train your brain and establish new neuronal pathways.
PS: Here's what your brain, or at least the upper area of the neocortex looks like on Ne: it's like a Christmas tree lighting up, all areas firing more or less simultaneously. Your brain can also show this pattern for non-Ne activities: when you're drunk. :-)
I got certified in Dario's Neuroscience of Personality program last year, and highly recommend it. If you'd like to do it, find dates near you here.