How long does it take?

not direct you can get a bus from airport to the bus station in the city centre and then a races bus from there. I think the races bus leaves either 2 hours or 90 mins before first race.

whatever you do dont get a taxi!

get a bus into bus aras and there will be buses to racecourse, give yourself plenty of time.

don't get the racebus from dub. normal , early, bus to naas and enjoy a few pints in town . taxi to course will be about 20 euros ...back into naas after , buses back to dub run fairly late. let all the traffic die down . i've done it loads of times .

has anyone an idea how much a taxi from naas to the city west would cost

Get the green Dublin coach to Naas, one leaves the airport every hour, and then get one of the shuttles from Naas that takes people to the course (leave every 10 - 15 mins).  Will cost you 10 euro for the Dublin coach & am guessing probably 6 euro for the suttle, i.e. 32 euro return.