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What are the procedures to apply for a travel visa?
You would need to apply for a regular tourist visa at the nearest Irish consulate. You can find a detailed guide on how to apply for a visa at the Irish INIS website.
Is it possible to apply online or are there provisions to get an on arrival visa in Dublin?
Citizens of certain countries may visit Ireland visa-free, however there's no such thing as an "on arrival" visa for other nationals, including Indians with a German residence permit.
You may apply for a visa online (see my link above), however you would still need to visit the consulate to submit your documents and undergo an interview.
I have Ryanair flying to Dublin from my city and I would really like to go to Ireland.
While you may not visit Ireland visa-free, having a German residence permit is a great way of showing you are unlikely to overstay your visa and therefore your chances of getting a visa are very high.