If you are based in the city getting to Blarney is quite straightforward. The 224 bus leaves the Bus Station at Parnell Place almost every hour and the journey to Blarney takes approximately 20 minutes.
During the main tourist season, the Cork City Hop-on-Hop-off Tour takes in Blarney as well. This is not the best option for visiting the castle though as the stopover in the village lasts only an hour and a half.
There are many organised tours from all over the country which have Blarney as a destination including a rail and bus tour which can be taken from Dublin.
If you are driving from the city take the N20 in the direction of Mallow and Limerick and you will get to Blarney directly.
I have not given bus times or prices as both are subject to change.
The buseireann website will have all the current details. A word of warning about bus travel in the summer, especially at weekends. Get to the bus stop in plenty of time as somemtimes there are more people than can actually fit on the bus and you may get left behind.
the bus to blarney is the 224 but you dont get the bus at the bus station in cork but just a little along from the bus station on the merchants quay near to marks and spencers, you will see the bus stand, tickets available on the bus or from the ticket machine in the station