Hit create, selecting the 3d design tab. You will be met with this workspace.
There are numerous tutorials for a variety of modelling skill levels within TinkerCAD
https://www.tinkercad.com/learn/designs?collectionId=OSZ5W2BL1W5N51F
Simple things such as object placement, viewing and manipulations tutorials are available at the top of the tutorial menu.
More advanced skills are available the further down the tutorial page.
TinkerCAD also allows for the import of other 3d models (stl, obj and svg file types up to 25 MB in size) for in browser manipulation.
To save your design to your device, select the export button in the top right of the tinkerCAD page. A selection menu for which file type will be prompted.
Make you selection based off how the design will be used. 3d printed, laser cut, etc…
For 3d printing, select file type. Once the preferred type is selected, the file will automatically download to your device.