The featured items modules should be able to detect the images automatically and resize them.

Occasionally there are problems: these are nearly always due to mistakes in the image path and file name, which mean that the module cannot read the image file in order to resize it.

The things to check are:

1. You are using relative rather than absolute urls, eg images/stories/image001.jpg, NOT http://www.mysite.com/images/stories/image001.jpg. The module can often handle absolute URLS, but relative URLS are much less likely to lead to problems.
2. Remember that file names are usually case sensitive, so check whether you are using image001.jpg or image001.JPG for example. These are not the same, and using the wrong one will mean that the image will not display.
3. Don't have spaces in an image file name.  If there are spaces it is not a valid URL, it can cause problems reading the image file, and you will need to replace the spaces with another character such as '-'. This is what Google recommend, they interpret this as a space. The confusion comes about because the Joomla editor will upload images with spaces in the name, and link to them by replacing the space character with '%20'. This is not good from a search optimization point of view though, because it is not a valid URL.
4. Make sure that you have not put any leading or trailing spaces by accident in your image tags, for example if you use the html code <img src="/images/stories/image001.jpg " /> that will cause problems because there is a trailing space.

These are all good practice anyway, so it helps to get used to doing things this way. The confusion arises because image URLS are a lot more forgiving of mistakes than file names, which have to be exact, so an image may display correctly in an html page even if there are mistakes. However these mistakes will make it impossible for the image file to be read by the module.

Other reasons why there might be problems

1. You have an article read-more link before the image. In that case the image will not display because it needs to be in the intro part of the article in order to be detected, so you need to make sure it is in the intro part of the article.
2. Your server does not support the GD graphics module. In that case you will not be able to use GD for image resizing, so you need to disable that parameter in the module admin.
3. The file permissions are incorrect on the script which resizes the image thumbnails. This script is called resize.php and is in the module assets folder. Usually this script will run with permissions set to 644. Occasionally, depending on your PHP configuration, this may need to be set to 755.