Usually the image host will have form where you can select image files from your computer to upload. Once you have submitted your image files to upload, they will be then transferred to the image host's server. Some image upload forms are more advanced and can let you upload multiple files in one go, transfer for URLs and more.
Once your image has been uploaded, you will often be shown various ways in which to share or show your image to others, such as BBcode linking, galleries and normal HTML code links.
In most cases, the image host will put a restriction on the maximum image size allowed or the maximum bandwidth allowed. If you have a lot of images to host, then it would be advisable to opt for paid image hosting which will give you more space, more bandwidth and relaxed upload restrictions.