Open the gallery
An empty gallery shows a large Drag photos here area in the middle of the page and an Upload photos button at the top. Once the gallery has photos, that area goes away, and you add more with the Add photos button in the bar above the grid.

Choose your files
Clicking the area or the button opens your system's file picker, where you can select many photos at once. On a computer you can also drag files: onto the area in an empty gallery, or anywhere on the page once there are photos (you'll see "Drop to add photos"). Supported formats are JPG, JPEG, PNG and WEBP.
Watch the progress bar
The progress bar shows the percentage of the whole upload, not of a single file. Your browser sends three photos at a time, in two parallel streams, so hundreds of files go through smoothly without one huge request.
Wait for processing
When the upload finishes, the photos appear in the grid, some of them labeled Processing.... That's a normal step: a preview with your watermark is being made in the background. Your client sees a photo only once it's ready.