Hi
petkum and welcome to the forum!
Firstly, make sure that your image is in an RGB format and that it is editable. IOW words, if you open it up and it says "Index", go to Image>Mode and click on RGB. Now your file will say
Background with a little lock icon on it in your Layers palette. To unlock and make the file editable, just double-click on the layer in the Layers palette.
You you will have to remove the white background from your logo. If it's a solid white background, the magic wand tool should do a bangup job on making a selection. Just click on the white background area of your image and hit
delete.
You can export your image as either a GIF or PNG file, the only two formats that support transparency, for your purposes. To lessen the "jaggies" around your logo, you should matte your file with a colour to match the background that you will be putting it on.
I hope that this helps and answers your question. If you have any problems, don't hesitate to ask some more.
Enjoy PS and the forum! [excited]