Open your image and paste it on a new Photoshop Document (Ctrl+A, Ctrl+C, Ctrl+N, Ctrl+V).
Now we make a new layer on top of the image:
Take the gradient tool 
, and on the top select the gradient you want to use. I selected one of the rainbow ones, like it's shown below:
Click on a corner of the image and drag to the opposite corner (just like you would use the gradient tool normally). Your gradient should appear now.
We need to change the blending mode for that layer now, change it to "Color", almost on the end of the list.
Now it's done! you've got your image colorized.
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