Well, Aragorn, I've written several First Age fics, some of which are posted here at the Downs, and others which are up at Fanfiction.net (here's a link -
Ithilwen's authorpage.)
I found that what inspired me were questions or challenges concerning specific characters, such as why did Maeglin betray Gondolin (and is it possible to show him in a sympathelic light), and why did Maedhros change from being a noble Elf to someone who was willing to commit mass murder. You need to write about what appeals to you. I'd suggest you ask yourself what it is about Aragorn's time as Thorongil that you find interesting, and work from there. Are you simply curious about what adventures he may have had (in which case you're looking to tell an exciting adventure tale), or is what interests you the effects his adventures had on him as a person (which would be a more psychological story)?
As to how to write it, there are no easy shortcuts - it's work. If you don't have someone else who can read you fic before you post it (and I didn't when I first wrote mine), I highly advise throwing the thing in a desk drawer for a week or two after you finish it. When you take it out again and re-read it after that 'cooling off' period, you'll see the flaws in the story more clearly, and you'll find editing it is easier.
Good luck writing your fic!