On a Windows computer, hold down the Ctrl key and click on each image that you want to delete. After you have selected the images you want to delete, press the delete key. You will be provided with an option to either remove or to delete from disk. If you remove the images, they are simply removed from the catalog but remain on the disk. If you choose to delete from disk then the images are removed from the catalog and deleted from the disk.
Another option is to highlight the images that you want deleted. As you browse through a group of images you can simply type the letter X as each image is displayed. When you have finished browsing the images just hit Ctrl/backspace. Lightroom will display all the images that you have marked for deletion, and will give you the same options described previously.
If you are in grid mode, deletion applies to all selected. if in loupe mode (or develop module), delete applies to one image only (regardless of how many are selected), unless you go down to filmstrip and context-click selected photos and delete using popup menu.
PS - In my opinion, photo targeting is the single most confusing aspect of using Lightroom. I've been at it for years and I still get mixed up sometimes. There are some general principles, but also gobs of exceptions...
Tip: If you want to circumvent the prompt, use "Splatt"-Delete:
On Windows, it is: Ctrl/Alt/Shift-Delete.
On Mac, probably: Cmd/Option/Shift-Delete.