It is possible to pay only $0.01 for a keyword (rare - yes; possible - definitely).
Minimum bids for keywords depends upon the 'Quality Score' of your Landing page as dtermined by Google. So your competitor may be paying 1 cent while you may have to pay USD 10.00 for the same keyword if Google decides your website landing page does not provide a useful user experience.
You need to set up advertising under the AdWords program , add keywords, check the minimum bid prices allocated to your keywords ( as applicable to your site, determined by Google), and then take a decision.
