You just follow signs for transfer flights and you will enter the departures lounge. You go through Irish security, but not immigration. You then follow signs for the USA Pre-clearance area (signs have American flags on them) and you enter the dedicated part of the terminal. You will pass through TSA style security first and then join the line for the pre-clearance area. After that you will be in a sealed off part of the departures terminal with a few shops and bars, although there is no duty/tax free as you will technically have already crossed into the USA by this time, so make sure you buy any before entering the pre-clearance area.
When I flew EDI-DUB-ORD, all on one EI ticket, I did not pass through Irish immigration. I stayed airside the whole time.
When I flew EDI-DUB-PHL with two separate tickets, changing terminals, I did have to enter the ROI and then leave again, but I had a bag to collect. I am not sure though if you can stay airside and transit while needing to change terminals at DUB.