The trick to editing watermarks is knowing that watermarks are usually part of the header, even though they appear in the middle of the page.
Double-click near the top of the page, to open the header.
Click the watermark to select it.
Now you can drag the watermark to change its position on the page, and you can edit it based on what kind of watermark it is.
If it's a text watermark, you'll have the WordArt Tools tab available, and if it's a picture, you'll see the Picture Tools tab when the watermark is selected.
If it's a text watermark, you can drag it to change its position on the page, but no other editing.
If it's a picture, right-click and choose Format Picture.