Creating a ZIP file: Simply click once to select the files or folder you want to put into the ZIP file, right click and select "Send To" and then "Compressed (Zipped) Folder". The ZIP file will be created in the same directory as the selected files and will be automatically named the same name as the file or folder you right clicked on, but with a .ZIP file name extension (if you have them visible in Windows).
By the way, if you select more than one folder, just right click on one of the folders and follow the instructions as listed above. All of the folders will be included in the zip file. You can rename the ZIP file after if necessary.
You should also be able to create a blank ZIP folder by right clicking on your desktop and selecting "New" and then "Compressed (zipped) Folder" and then draging and droping files/folders in or out of it.
You can also delete files right in the zip file almost as if they were regular Windows folders.