Sticky posts will stay right where you stick them.
Your homepage automatically updates to feature your newest content. But if you want something to stay featured even after newer posts have been added, there is a way.
Go to Publish in the upper left of your dashboard
Click Blog
Find the post you want to stick and click Edit, or you can hit Add New if you haven't yet created your future sticky post.
Scroll down to Publish
Find Visibility and click Edit
Check the box marked Stick this post to the front page
Done! That post is on your homepage to stay forever, or at least until you go back and un-check that box. :)