Hey,
I have just installed Inkscape today, thus please forgive me for asking a super beginner question. What I want to do is to create a logo which has a specific size. I also want the background of the logo to be in a specific color. How can I achieve this? I tried to search for my question(s), but probably I used the wrong search terms as I couldn't find the answer. Thanks a lot!

-- Open Inkscape, and pick a tool, let's say the Ellipse/Circle tool, and draw a circle
-- Switch back to the Selection tool, and using the W and H fields on the control bar, set the size you want
-- While the circle is still selected, click some color on the palette (near the bottom of the window). Or if you want a custom color, use Object menu > Fill and Stroke

For the rest of your logo:

See Help menu > Inkscape Manual
Also see Help menu > Tutorials
Also see the links in my signature (the stuff below this message, which has red text) for more tutorials
Also see LMGTFY (let me google this for you)