ConseilWeb’s method will work if you want the latest post published on the home, but sticky is a bit different.
There are several ways to do it but, let’s take one of the easiest :
1) Create a template variable (type checkbox) called "promote_to_frontpage" (to do this go to Resources > Manage Resources > Template Variables, then "New Template Variable". In "Input Option Values" just add "sticky". Set the default value of "not sticky". Assign to your template. Now you can tick or not the sticky checkbox when editing a document.
2) Place a Ditto Call on your front page :
[tt][!Ditto? &parents=`id_of_your_news_folder` &display=`1` &filter=`promote_to_frontpage,sticky,2`.... other classic parameters... !][/tt]
If you want several containers included, just type in a list of IDs [tt]&parents=`12,34,66`[/tt]
[tt]&display=`1`[/tt] you can change this if you want to have several stickies

About &filter, check
Ditto’s doc about filters for more details
This should do the trick (unless I messed up the filter mode again

).