Sorry, your message was overlooked.
You would have to prove that you have held the job for several years, that it provides a livable income and that you won't become a burden on the Irish state. That means providing materials like three years of tax filings, letterhead notes from the company(ies?) that employ you explaining the setup and that they are happy to continue employing you, bank records showing that you have funds, health insurance that will cover you in Ireland and such.
You would get permission to reside her for one year at a time and you would renew every year for five years. At the end of five year's residency you could apply for either permanent resident's status or citizenship. There are no guarantees on those annual renewals - policy might change - but generally it's all pretty automatic after the first year's approval.
Start with the Dept. of Jobs, Enterprise and Innovation (fancy new title for the old Dept. of Enterprise) at http://www.djei.ie/
Best of luck,
: Let's say that you have no 'good' reason to
: move to Ireland. You just like the culture,
: the people, the weather, and the place
: itself. Let's also say you are 100%
: financially self-sufficient, well-off, due
: to a job that takes place online.
: Is it possible to move to Ireland with these
: conditions? If so, what's the process of
: attaining citizenship, and which 'reason' do
: you file under with the Irish immigration
: service? I looked at the immigration site
: but it's long and complicated and I don't
: know where to start.