creating a custom 'read more' button in post

hi there! i think i have found the end of the internet trying to figure out how to do this, alas i still am totally stumped. i want to use a custom graphic that i have created for my ‘read more’ page break in a post. essentially i have just made a nice looking ‘button’ in photoshop and uploaded it to my media library. instead of text saying ‘read more’ with a hyperlink to the full post, i want to be able to have the button show (which says on it ‘continue reading’), and have the button, when clicked on, link to the full post.

i hope i am describing this process clearly because it seems like it should be simple and easy to do (so far for me, its not!), and i also can’t find a plugin which does this, which seems a bit odd to me (i feel like this is a common want?)

I’m using the lynette theme by bluchic, and the latest / 4.1v of wordpress. my site currently has a privacy filter on it (while i am building it) but i can take it off if it would help get some help. Thank you!!!