There are a few ways to hang your planter in your home.
First is directly from the ceiling. It's best to use a drywall anchor that you can screw your hook from so it is secure and can hold a heavy plant. Some drywall anchors you can screw straight into the wall, others you have to make a hole first and then push them in. There are a few different options of hook you can find at your local hardware store. Keep in mind, if you can't find the colour you want you can always spray paint it before you screw it into the anchor.
The other option is to hang it off your wall. You can find wall hooks or brackets that get mounted on the wall. By using something like this is will allow your plant to hang and not be smushed up against the wall.