Select your logo/curve in AI.
Save As SVG.
Import SVG into Blender.
NOTE: The quality of the SVG import is only as good as your AI curve. So if you are a novice at AI you may be created bad input. The simplest test is to simply type a letter in Illustrator, convert to outline, then save as SVG.
Now import the SVG file and you should see the curve from illustrator. IF you do not have faces when you extrude, your curve is either open or bad. IF the curve is open, simply press the C-Key to close the curve. Sometimes this happens. If the letter you typed was a lowercase “p”, you will notice that you have two curves. the inner circle and the outer “p” shape. Select them both and press CTRL-J to join the curves into a single shape. Sometimes you can not see the inner circle of a letter “p” because the outer shape it on top of it so blindly right-click to select the inner circle.
Extrude is the final curve test. If you extrude the curve and it does not look right, or partial faces appear, Blender is telling you that your curve is messed up. Don’t fret, sometime a horrible looking extrude is only the result of a duplicate vertex somewhere. Simply select each point (hey you wanted to be a designer) and press the G-Key to move it around, observe the effect on the face. Press ESC to abandon the move on the vertex and it will snap back to it’s original location. Keep working through the points until you find the problem one, then delete it.
This is my trial and error workflow that I have developed, so you get the knowledge drop for free. Don’t give up, try a single letter import first then work your way up to a complex logo.