Hmm. I am not a Facebook expert, but since no one else has tried to answer this, I will say that yes, it should be easy to do this, but probably not even something you need to do in settings.
There should be a way to ask your friends to "like" your page. I get these requests from friends all the time. I have not started a page and done this myself, but I can tell you some of them are not very techy and could do it. This is not to discourage you- rather, if you don't see an option, you might Google search and even see a link to click and take you to where you need to be to do the same.
It could also be your settings, but if so, I would imagine you would see an option there to "invite friends to like your page".
Also, when you post on your page, is there a way to "share" it to your regular facebook wall?
Oh- and going back to the very beginning: when you said you have a Facebook page, I assumed you meant this is an author page, in addition to your regular Facebook profile.
I just recalled where assuming usually brings me, so if you are new to Facebook and mean you created a profile and want friends to see your post, they do just by you posting. You do have to have connected with a list of "friends" first. You either ask others to be your friend, or they ask you. Then they will see posts (and your settings may allow friends of friends to view the posts as well, depending).
But if you have no "friends" on your Facebook account, then no one sees the post.
But, if my original assumption were correct, and you have friends who can see your original posts but are just not seeing posts on your author page, then go back to my original instructions and either invite them to like your page, or "share" a post from your page to your FB wall where your friends can see.
That is all I know about it so far, unless or until others chime in to add or correct my basic suggestions. Best wishes.