You can take the Dart in any of the stations in the city center. He Dart It is the commuter train and has a route ending in Howth, so it will be impossible for you to pass the stop. You can take the Dart in the following stations: Connolly Station, Tara Street Station, Pearse Station. The price of the round trip ticket from Dublin to Howth is € 3.80 and the journey takes between 25-30 minutes.
There are 2 bus lines that reach Howth, the 31 and the 31B. Both have the beginning in the same place, Eden Quay, located near the street O'Connell (if you go down O'Connell in the direction of the river you must turn left just before reaching the bridge O'Connell Bridge, there you will begin to see bus stops aligned and you will have to find the bus stop 31 and 31B. The price of the ticket is € 2.10, one way, and I advise you to take change in currencies to be able to pay the exact amount since the driver will not return the change in coins but it will give you a paper so that you go to collect your 10 cents or 20 or those that are to the central office; We are going to have a pain, and a good way to fill the coffers of currency in currency since I still do not know anyone who has gone to claim their change to the bus offices in Ireland.
Here are a couple of links that may interest you:
How to get to Howth by train
How to get to Howth by bus2.001