The Schaum outline series book by Spiegel (1992) provides a very readable (and affordable) basic introduction to univariate statistics. The books by Wilks (1995) and von Storch and Zwiers (1999) go much deeper and present many of the statistical methods used in atmospheric and climate research.
To develop a deeper knowledge of statistics, it is also worth starting a dialogue with professional statisiticians by browsing the links to statistical sites and organisations below. Remember that its most likely that you are not the first person to have used a particular method and that there is a wide range of statistical information and advice available in text books or via the web. There is no excuse for not knowing about the method you have used to analyse your data - good artisans know how to use their tools properly !
http://www.stats.gla.ac.uk/cti/
Good collection of web links to many useful statistics sites
http://www.statsoft.com/textbook/stathome.html
StatSoft Inc.'s Electronic Statistics Textbook
with brief comments on a wide range of
topics from basic to advanced, including variance components,
neural networks, multidimensional scaling and so on.
The emphasis is on techniques rather than concepts or mathematics.
http://davidmlane.com/hyperstat/index.html
David M. Lane's HyperStat Online introduction to statistics.
http://www.york.ac.uk/depts/maths/histstat/welcome.htm
Some more information about the history of statistics.
http://www.math.uio.no/nsf/web/index.htm
The Norwegian Statistical Society.
http://www.rss.org.uk/
The Royal Statistical Society.
http://www.amstat.org/
American Statistical Association.
http://www.stats.gla.ac.uk/cti/activities/reviews/alphabet.html
Informative reviews of many different statistical packages
http://lib.stat.cmu.edu/ StatLib index of statistical software and routines
http://members.aol.com/johnp71/javastat.html
John C. Pezzullo's nice collection of interactive statistics scripts