Create two layers in your photoshop file, which has the same dimension as your image, for ease.
With the first layer fill it with say Lime green... the second layer being your image you want to remove the background on, so copy and paste your image into that layer.
Choose layer 2 and then the brush tool from the toolbox on the right. set it to 5px from the dropdown choices (not the first one marked 5, but scroll down and choose the 2nd 5px one) this one will give you a nice antialiased edge around the image. Once selected on the toolbar at the top you have other options, namely mode: you need to change this from normal to clear.
Zoom in on the image and start tracing around the image with the brush, everything you mark will become lime green around the image. When you have completed tracing around the image you can then lift that layer without the background wherever you want and place it on any image background.
If you want any help give me a shout