What is the Magit equivalent of
git add [--intent-to-add] <filename> for checking a newly created file into Git?
To stage a change press s with point on any "stageable change". This includes files listed below "Untracked files" and "Unstaged changes".
You can also expand the files below "Unstaged files" using TAB (also works for many other sections) to see the hunks. You can then stage an individual hunk, again by pressing s while point is inside it.
You can even stage just parts of a hunk using the region. To do that press C-SPC to mark the beginning of the region and then n a few times to move to where the region should end.
In order to
git add --intent-to-add, use C-u s.
You can also unstage, discard, reverse, and apply changes in a similar fashion. This is described in more detail in the manual. In particular see Staging and unstaging, Applying, and Sections. Staging is also covered in Getting Started.