The way this forum (and the blog comments) pulls avatars is via Gravatar (Globally recognized avatars). I installed a plug in a couple years ago that assigns you a random coloured square with the first initial of the name you’re using so everyone isn’t just a grey head icon, but if you want to choose your photo, sign up with Gravatar using the same email address you use here, and that photo will follow you around the internet, including here!
You'll need to upload them to a free image hosting service first—Imgur (http://imgur.com/) is great and doesn't require you to sign up for an account. Simply click " New Post" at the top of the page, drag your images into the window that pops up, and the images will automatically upload. From there you can hover the images and copy the URL that appears; simply paste that URL into your post on a new line and the image will appear automatically when you post!