You can easily save your project in Qgis. Whenever you close Qgis, you are automatically asked if you want to save your project. You can also save your project before you exit Qgis:
Go to Project in the menu bar
You can only open a Qgis project in Qgis to continue working on it. If you want to use your work in another GIS programme, you are advised to save the layers as shapefiles. If you want to use a map image in a report or presentation, you are advised to export a Print Composer as an image.
Every layer, including all possible data processed, can be saved as a shapefile.
Go to the Layers Panel on the left side
Right-click on the relevant layer
Click on Save as…
Select Esri Shapefile
Choose a name and a location
Click on OK
Print Composers belong to a project. As soon as you create a new Print Composer, it will be saved within the project in that form. When you save the project, the Print Composer will be saved too.