There are several methods to eliminate unwanted subjects or details from our photos. Today we'll see how to delete something from a photo using Clone Stamp, Healing Brush and/or Patch tools.
Clone Stamp
Clone Stamp is used to clone a certain area of the picture.
Clone StampHolding ALT key you select a referencing area to clone. The clone tool will select this area as source. Release the ALT button and move the brush to cover the area replacing it with the cloned one.
The clone tool is useful to delete blemish, spot or dust. It makes an exact copy of the pixels without any merging of the surrounding pixels.
If you are planning of use this tool for a more extensive area of the photo you may need to re-sample the brush from different areas around your subject, changing the tool size several times. I strongly suggest to do that because copying a huge portion of the canvas will reveal the fake. The eye is well trained to take note of apparently insignificant details.
Healing Brush
The healing brush tool works similarly. Despite of the Clone Stamp it performs some blending, trying to match light and shadows and even the texture of the area. Using the healing brush the correction will be better merged with the background. This make the effect looking more natural.
Healing BrushWhy then still using the clone tool and not to use the healing brush in place every time?
The answer is easy. Because of the healing tool makes a blending merge with the background it leaves behind spots and parts of what we want to conceal.
What is the best way?
As usual there isn't a one-way procedure, it strictly depends on the image.One of the best way is firstly operate with the clone tool to 100% cover the area, than, using the healing tool, conceal the artifacts of the cloning operation.
Zooming and changing the tool size is very important because you need to have an inside glance into the area that you want to retouch.
Let's see a practical example.
Warning! Always duplicate the layer you’ll be working on! So that you can easily coming back or recovering cloning mistakes.
You have this photo of the Miyajima Shrine and you want to clean up the two men.The man on the left is easy to remove compared with the man on the right that casts its reflection on the pool surface.
This is an important point. ALWAYS be attentive and check for tricky reflections!
Is not a good job if you remove something leaving back shadows or reflections.
So, firstly use the Clone Stamp:
Make changes to size, hardness and opacity in order to reach a soft result.
The man has disappeared but we still have to cover the excess of smoothness and his shadow casted on the shore.
To do that we need a change of tool.
Select the Healing Brush, sample a similar area and cover the artifact.
Do the same with the second man.
Patch Tool
Similar to the healing tool is the Patch Tool. It works in the same way but you can select and retouch extensive areas. 
Patch ToolThe Patch tool combines the selection behavior of the Lasso tool with the color-blending properties of the Healing Brush tool. Again it makes a blending with the background so, in some occasions, it could be necessary to cover the object before or adjust using Clone Stamp and Healing Brush tools.
So the final result, the two images compared.
Other resources about this topic:
The Ultimate Guide To Cloning In Photoshop
Use Photoshop's Healing Brush And Patch Tool To Remove Wrinkles
How To Mirror Your Clone Stamp - Photoshop Cloning Tip From John Nack - Plus Video Tutorial From Russell Brown
Retouch with the Healing Brush tool
