Umm find an image you like. Right-click, properties. Copy image location. Write your post or whatever & paste in the image location in the appropriate tag (img). That's pretty much it. The image will be shown on your site, but is actually being served from the other site. Just be aware, that many webmasters (myself included sometimes) add htaccess rules to change images when they are hotlinked.
Several years ago, a local private school had hotlinked an image off one of my sites and even after I contacted them refused to change it. Hell I even offered to email them the file. A quick rule change later (I love apache!) everyone who loaded their page got a picture of the goatse.cx guy (google it) instead of their logo. It took about 3 hours before I got a phone call from the dean threating to sue me because in the words of their "computer guy" I had hacked their site. He calmed down once I told him about the previous email exchanges and told him he was welcome to sue but to expect a counter suit for theft of my IP & bandwidth charges.