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I have this image of the logo of my NGO and I want to use only the part of the actual logo (without the white background) so that I can put it on photos/flyers etc. I hope I could explain it clearly enough.
How can I do this? I have Photoshop CC 2015
Fairly straight-forward image to work with.
Realize that if you want high-quality image you can scale to any size, you'll need a vector version of the logo. Using that particular PNG is never going to result in a high quality image. At best you can get an image the same size or smaller without the background. Anything else would require recreating from scratch in a better format.
To get rid of the background in that particular image it just takes a few steps with Photoshop.
Image > Adjustments > Levels. Click the Auto button, then move the left slider (white) to the right until it is inside the little black peaks you see. Then move the right slider (black) to the left so it is inside the little black peaks on the right. and click OKNew Layer Mask button on the bottom of the Layers Panel.
That should provide an image with the background masked out. You can save the image as a PNG to retain the transparency, or add new layers below the image layer with any color you wish.
You can double-click the Layer mask in the Layers Panel to further refine the things as needed. In some cases there may still be a slight color matte around the image. So refining the mask is necessary.
Blending Options can make short work of this. Just go to Layer → Layer Style → Blending Options. At the bottom where it says Blend If: Gray, This Layer you'll see a slider.
You can read that as "Make transparent if this layer is this black or this white". Pull the right side in a tad and you're done.
For laughs, I made this. In your instance, you have a shape defined by two clean ovals overlapping. If you wanted to be quick about it, you could pull it out like this... but as mentioned in Metis's answer, it's not a vector, so it won't scale well at all. If you have access to Adobe Illustrator, now would be a good time to get familiar with the basics of that program! ;)
Your photo has low resolution. Its good for onscreen purposes, but it allows high quality printing only as about 2,5 cm wide total. Fortunately we can easily increase it to 7,5 cm without very bad quality loss.
The ellipses seem to be even more unsharp than the low resolution alone would cause. We can fix the ellipses at the same time when we remove the backgroud. I assume that you want to save te white inside the ellipses as the color of the smaller shapes.
1.Take the elliptical selection tool and draw a selection over the leftmost ellipse. Goto Select > Transform Selection and drag the ellipse perfect. finally press enter to fix the selection for use.
Take the smudge tool. Push the blue color against the selection around the selected area. You fix a little of the unsharpness.
Press Ctrl+C (=copy), goto Edit > Paste Special > Paste in Place. You get the left part as a new layer without the background (in the screensot the selection marquee makes the border unclear)
6 We have one trick left: Enlargening. It needs appropriate software, in this case ON1 perfect resize. It can enlargen drawings and often even photos without the same loss of apparent sharpness than scaling the image bigger in Photoshop. Of course it quesses the missing detail, but in easy cases it succeeds. Here's an example. The enlargening (300%) is done first. The ellipse borders are cleaned by pushing the color with smudge against the selection when the halves were copied. Not perfect, but maybe usable:
Warning: This is PNG with transparent background. If you copy it and paste it to Photoshop, you probably get black background. Download it, then it works better.
