You need to read and understand https://developers.google.com/drive/v2/reference/files#resource and https://developers.google.com/drive/search-parameters and https://developers.google.com/drive/v2/reference/files/list
At the bottom of the last page is a Try It Now feature which you can use to play with the Drive SDK BEFORE you write a single line of code. Do the same with https://developers.google.com/drive/v2/reference/files/delete
Once you understand them, you will know how to trash or delete files from Drive. Personally I prefer trash as it's easier to undo my mistakes during testing. @martineau Don't worry too much about the disk space; Google isn't about to run out of disk :-)
The only catch to using Trash is you need to remember to qualify any queries with 'trashed=false' and users will need to empty Trash if ever they hit quota.