The best free hosting site I have found is Imgur. It is free and they have never deleted an image I hosted with them. I don't log in and I don't have an account. We have a limited number of attachments we can have in this forum and still keep it free so please upload images to an outside host and then post the share links here.
To get started on Imgur you Click "New Post"
Then this box will popup:
You can either navigate to the saved image in your computer or copy the image or the images url and past it into the box. The url must end in a digital pic type ie; jpeg, png, jpg.
If you copy the image url you right click on the image and it will bring up this menu or similar depending on the browser you use. Choose the option I have indicated. You will want to copy that link into the paste image or url box above.
Once the image is uploaded just hover the mouse over the picture and the direct link will appear. These options are the same no matter how you uploaded the image.
If you hover over the down arrow the menu pictured above shows up. Click "Get Share Links" and the below menu will pop up.
You want to choose the BBCode (Forums) link to share a picture here. It shoud start with {img] image url [/IMG] (change the { to ] for it to work.