When you are viewing the Activity Details screen for an Activity, you'll see a Linked Documents area:

 

 

 

Just click the add button in that Linked Documents area. You'll then see an Upload Documents modal:

 

 

You can then click the "Add Files" button to browse for the file on your computer or drag and drop the file into the upload area. The "Start Upload" button will then be available for you to upload the file.

 

Once the upload process is complete, the file will be accessible for download in the Linked Documents area of the activity's Details page. Note: documents linked to Activities are also linked to the Document Storage Area for contacts linked to those Activities.