Note: I'm not an experienced Photoshop user. I know next to nothing about Photoshop but I was presented with a task and this is how I solved it. There could be easier, faster and/or better solutions but this one worked for me.
There's no "single click" solution to create rounded corners for your photo (or some other image) in Photoshop. There are several ways to achieve this effect with "rounded rectangle" method being probably most popular. At least it is the most popular in Google search for "photoshop rounded corners". In short: you just draw a path using rounded rectangle tool, make selection out of it, inverse the selection and delete what's left.
This is all fine when you need to do it once. But what if you need to do it multiple times on images of various orientations and sizes? You can create a simple "Action" to repeat these simple steps but you will be stuck with a fixed size.
In short: my solution was to deal with one corner at a time, rotate the canvas and work with the same corner which is now actually not the same corner and so on.
Here are the "Action" steps in detail:
This is our original image
1. Open your image and select "Rounded Rectangle Tool"
2. Select "Paths" as drawing method
3. We select a desired rounding radius - 10px in our case. Now we want to work with only one corner so we have to make the rectangle larger than the image. And since we are recording an "Action" we need to make it fixed size. I made it 5000x5000px (picture shows "cm" but that's too much and I was too lazy to make another screenshot)
4. We place our rounded rectangle by the top left corner of our image
5. In the Paths palette select "Make Selection..."
6. In "Make Selection" dialog leave the defaults (unless you want something else) and click OK
7. Inverse the selection and we have our rounded corner selected. Now just delete the selected contents
8. Now we rotate the canvas by 90 degrees in your preferred direction
9. Repeat steps 4-8 three more times and you are done. Here's the result
Here's the "Action" to automatically create 10 pixel rounded corners for images of any dimensions and forms (up to 5000x5000px). Download rounded.zip (0.5kb)