Depends do you wan't to work in it professionally or it will be just for learning...
There are two mayor players in vector art:
Adobe Illustrator and Corel Draw, both of them are very good programs for vector art, while Corel is more 'easier' to learn, if you're asking me.
You can find tutorials on YouTube.
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But, if you are short on cash and you want to learn through freeware stuff, InkScape is your thing.
Last edited by Django77; Mar 30, 2013 at 12:39 PM.
Reason: <24 hour edit/bump