When performing a search in Google Drive the results will show documents you have created, documents that have been shared with you, and documents that you have opened but are not shared with you.
From the search results you are not able to drag the file into a folder. Instead single click on the file.
Add to Drive
After selecting the file you will notice an “Add to My Drive” icon in the toolbar above the document list. Choosing this icon will allow you to file the document into a single folder in your Drive. If you want to add that file to multiple drives use “Shift Z.”