Irish is one of those languages which seems to have a very big disconnect between how it is written and how it is spoken. This makes learning it from a book a little difficult. It's a language that must be heard to get a handle on its spoken form. Once the spelling conventions and basic pronunciation are learned, it really isn't that difficult. Luckily, Irish is having a resurgence before the language was really endangered, like some of the other Celtic tongues.
There are a number of online sources to get an early start learning Irish, and there are a wide variety of general resources to use it once you get going.
Internet/Free Learning Irish A whole bunch of lessons in order with lots of pronunciation clues and vocabulary. Mostly designed for Americans, with their pronunciation particularities, learning Irish on their own.
Internet/Free Interactive Irish Grammar-based tutorial for learning the Irish language. It has some reading practice and accompanying audio.
Internet/Free Irish Gaelic Lessons Online Another free tutorial for learners. It's grammar-based, has basic vocabulary and reading practices from Irish literature.
Internet/Free Transparent Language offers a free vocabulary trainer to get started learning Irish - Free Before You Know It™ download
Teach Yourself Irish
The longstanding Teach Yourself series is one of the very few publishers with a readily available course for learning the Irish language. There is a coursebook which also comes with two audio cd's so you can begin to learn the tricky Irish pronunciation!
Transparent Irish Premium uses native speaker audio, text, video, games and dialogues to immerse you in the Irish language. With 15,000 words in mp3 format to use in your iPod or mp3 player and it can be fully integrated with BYKI. And, there is a six month guarantee. Overall, a great resource to learn Irish!
Other online resources for learning Irish Gaelic :
IrishGaelicTranslator.com Has a very good and very active forum for people learning Irish. Get your questions answered by a native speaker, or a tricky phrase translated. Also contains some resources for continued study.
Beginners guide to Irish Gaelic Pronunciation. A very basic pronunciation guide for Irish. A quick one-page rule-of-thumb overview of pronouncing Irish names.
Beginners Blas BBC's site for learning Irish. Includes audio lessons and links to all kinds of general resources.
Daltai na Gaeilge
Lots of resources for learners. Phrases, proverbs, games and lots of short articles written in Irish for when you are ready.
Lots of great features to help you learn Irish - a word of the day, flashcards, audio, dictionary, games, a forum and more.