To create a new project, start by selecting a task and going into edit mode. The first tab is the Info Tab, and on the right side you will find the project picker. To add a new project, simply tap to focus the input field which will bring up the keyboard. Type your project name and click the add button. Notice how the project is automatically selected for you. Context's and tags are added the same way, but on different screens. Context can be found under the filters tab, while tags has a dedicated tab all to it's own.
There are slight differences in the way tags are handled versus context and projects. While. context and projects can have only one item selected, tags can have many items selected. So as you add new tags they each become selected and thus applied to the task being edited.