Result:
Click here to view!

1. First you need an image to make your Multi-Colored Effect on, I will be using this image:
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2. Now that you have your render/picture or whatever, lets get started. Lets get us a color that we want to use to blend, I will use Red #FF0000. But you don't have to use this color.
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3. Next we will make a new layer, ABOVE all color balanced Layers.
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4. Now make that layer as SOFT LIGHT. Like so:
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5. Now get your Brush tool (B) and pick a soft grunge brush so that the colors blend in nicely. I will use Rust 'n Grunge from this link:
http://www.deviantart.com/deviation/12075057/

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6. Now brush, preferably from the one of the sides. If you find that you brushed too much you can always lower the opacity.
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7. Now you can stop here, but if you want to add more detail and more blending you can always go farther by doing the same steps from 1-6 with a DIFFERENT color. I went on with 3 different colors and lowered the opacity of the blue abit so that red and yellow can be my main colors.
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8. Now once you've finished that, you can (OPTIONAL) add a color balance layer over all of the layers Layer>New Adjustment Layer> Color Balance. And you can play with the settings. If you don't like the result of the first color balance then you can always add another Color Balance Layer.
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This concludes our tutorial, you should have something similar to this:
Click here to view!

Some more examples using this tutorial:
Example 1
Example 2