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The interactive exercises at regexone.com are a very good place to get your feet wet. I definitely recommend starting here.
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This is a different interactive tutorial that I think is somewhat complementary.
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Also check out the resources including interactive exercises regexinfo.com regexinfo.com
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Also here for checking how your Regular expressions are working in real time. http://regexr.com/
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Here are two nice regular expression cheatsheets, here and here. Pick one of them, and print it out! It is useful to have a binder of your programming cheatsheets!