Your homepage is set up using panels and blocks which is different than your inside pages.
To access the blocks, mouse over the upper right corner of each block until you see the cog wheel appear.
Click on Configure Block, this will open the block so you can add content.
Site managers have the access to maintain these blocks.
The landing page may also include the slider. Directions can be found here.
If your landing page includes feeds for news or events, those blocks will auto-populate as you add your content.