Whats the best way to extract logos from a website or picture file for my own use?

This is not any form of copyright infringement. I am trying to get the "U" logo from the University of Miami to use as part of a organization's logo. The "U" signifies where we are from.

Its no form of copyright infringement. What I am trying to do it extract the image from the file so that there is no background to it. Similar to .png files.

Right click > copy > paste into image editor e.g. paint, photoshop > crop the areas you don't want and save.

If copying doesent work do a screen shot by pressing your 'Print Screen' button then paste and follow the same steps

As long as it's not violating any copywrite laws, you would simply right-click on the logo and select Copy. Then you would open up MS Paint and paste it on there.

U of Miami uses the Font Face "Century" Specifically Century Old Style. Since you can start with that as a basis for art work and it is already in vector format, my preference would be to start from that and make it into any color you want, any size you want, rasterize it to add effects like drop shadows and bevels.

Or you can just right click it and save/copy

P.S. If you need backgrounds removed, I can do that for you