Different watermarks need different approaches: text goes with Content-Aware Fill, logos get covered by sampling with the Clone Stamp, and semi-transparent marks have to be patched before any color work. All three cases are covered here, and every step works in an online PS too.
Ctrl+J. Don't skip it — this way the original is still there and a mess isn't fatal.Shift+F5 opens the Fill dialog, or find Edit → Fill in the menu. Under Contents pick Content-Aware, then click OK.Quick tip: if the area you select is too large or too regular, PS reads it as "the part that needs filling" and you get a blurry blob. So draw the selection slightly irregular — an uneven lasso path, for instance — and the result is much better.
That said, this method isn't magic. Watermarks that blend into the background, or semi-transparent ones, won't come out in a single fill. My own routine: run Content-Aware Fill once, then clean the details with the Patch tool (shortcut J), or run Content-Aware Fill again with a differently shaped selection.
I made my share of mistakes starting out too — I selected the watermark and just hit Delete, and got a white block. Back then I didn't know Content-Aware existed and assumed PS simply couldn't do it. Only later did I understand that you have to use the option inside the Fill dialog, not the Delete key.
Also, if the watermark sits on a flat block of color, say a white watermark on a light gray background, Content-Aware may not find anything to fill from. In that case the Clone Stamp is faster (set a source point, paint a couple of strokes), or select the area and fill it with a solid color sampled from the background with the Eyedropper.
Note: Content-Aware Fill runs on the duplicated layer. Don't do it on the original, or you'll have no way back after saving.
One last bit of voodoo: the font, color and opacity of the watermark all change how well PS recognizes it. If one pass isn't perfect, don't give up — try a few more times, or reshape the selection. And if all else fails, the Clone Stamp one small patch at a time is slow but steady.
Almost forgot: the online PS tool I mentioned, https://www.zaixianps.cc, also does Content-Aware Fill with the same steps. It's a bit slower in a browser, but for emergencies it's plenty.
That's my rambling for today. If you have your own watermark-removal tricks, share them — we all learn from each other.