This is how you open the markup tool:

1. Open a photo or other image you want to mark up in Photos.
2. Tap the sliders icon in the top right corner to open the image editing tools.
3. If you haven't used the image markup tool before, you may have to activate it before you can use it. Tap the circle with the three dots. Then tap the More icon to make sure that the black markup tool is activated and tap Done. Now you can use the tool by tapping the markup tool icon.
4. The three tools that are available is a drawing tool, a loupe tool and a text tool. Activate each by tapping their respective icon down left.
5. Press Done to close the markup tool when you are done and then Done again to save the markuped image.

Note that changes are saved to the original file so there are no copies. You can revert to the original image file by opening the image editing tools again and tapping Revert in the top right corner.

If the iOS markup tool isn't enough for your needs, take a look at Annotable.

If you have questions about the markup tool, ask them in the comments.