I am a graphic designer and on a daily basis i work with vectors.I started off as a kid not knowing anything myself but i did use: AAA LogoThat was my first step into the branding industry.However if you looking into long term work you will have to spend some moneyor maybe get the software from a friend.Programs i reccommend:Vector Programs:Illustrtor, Correl Draw, Freehand, InDesignPicture Editinghotoshop, FireworksVideo Editingrimier Pro, Sound Booth, After Effects
Usually I start my designs in Photoshop and then when I have a good concept I create the vector in Illustrator.
IF you are talking about the software Illustrator is the best one for me. If you want to know about a specific tool in it than I use Pen tool a lot. and Rotate tool is fun to work with. But then again you need to work with a number of tools to get a good logo done.