I need a lot of help

Larry 
March 17th is a main holiday so some services are not running. 
But Dublin bus and the Luas will be operating. 
You cannot book  a train from Connolly train station to Heuston station. They are not connected.
 You have to get the bus or the tram.

 1 Book Belfast to Dublin.
 2 Get bus/ tram to Heuston pay on the day. A few euro.
3 Book train from Heuston to Galway.     Alternative to train is a bus from Dublin to Galway with  either Bus Eireann or Burkes Bus
 (not related to them Larry)                          or City Link.

1 Book Belfast to Dublin.1 Book Belfast to Dublin.1 Book Belfast to Dublin.file:///Users/gengsea/Desktop/Screen%20Shot%202018-02-08%20at%203.02.09%20PM.png
Look what I ended up there is no bus but rather a train and it shows a different time than what you told me

Why can you tell me which site to go where you found the schedule
that arrive to galway at 1:30 or so

 You said
book Belfast to dublin (which site iris rail translink?) translink won't let me put in a travel date beyond mar 7
get bus/tram to Heuston pay on the day. I guess I don't have to buy it in advance
Book train from Heuston to Galway. I like this option so which site can I go to book this 
I'm very frustrated and embarrassed bothering you so much on my stupidity

I think because I'm not in Ireland that I get diverted to translink. I found the train that leaves Belfast at 8:00 but when I click to book it I get referred to translink

I am so sorry for the confusion...
I hope I am correct , you are arriving in Dublin on 3/14 and staying for 1 night 
Then on 3/15 you are going to Belfast  3/15 and leaving on 3/17 
proceeding to Galway on 3/17 ,, if this is correct and you would prefer
the entire journey to be by train  this is what I would suggest 
Purchase your ticket as ( Return) from Dublin to Belfast for 3/15 returning 3/17 
Then purchase Dublin to Galway as single ticket 
I  have an example :
Dublin Connolly 3/15 7:30 am arrives Belfast central @ 9:45 am 
Belfast central 3/17 @ 8 am arrives Dublin Connolly @ 10:05 am
(Luas Surface )  departs Connolly  10:45 arrives Heuston 11:10 am 
departs Heuston 11:25 am arrives Galway 13:43 pm .
This would eliminate the Northern Ireland Train link .  

Larry
 Go to Irish rail.ie
I have just looked at the site. the 11.25 train will arrive in Galway at 1.40.

Input  Departures  Dublin  Heuston
         Arrival                 Galway

Single ticket 1 
Date 17th March.
There are three prices shown. The lowest price 16.99 is sold out but the 17.99 and 18.99 are available for that time.
The next train is 1.30 arriving at 3.40.
Don't worry about asking questions. It is confusing when it is not familiar
Mary.

My example was to make 2 separate bookings using Irish rail only
1 = round trip Dublin Belfast Dublin called return ticket
2 = single ticket Dublin to Galway is a one way 

Elizabeth has give you similar advice there.
 The only extra thing that I would advise is to get the Luas to Heuston from Connolly a little earlier. You need to arrive at Heuston by 11.00 to get your seat and queue up even with a booked seat. 
Allow yourself some breathing space.
 That train will be very busy. 
Mary.
PS I know you like the train journey but the bus and train times are very similar with Expressway Bus.
 Personally I would take the bus anytime before the train and it is cheaper.

I think I am going to try a couple of times then I'm not going to search anymore and take a chance to be stuck in Belfast.
Yes, Elizabeth you are correct about my itinerary. However, I'm not too concerned getting my ticket on 3/15 I hope it will be a lot easier. My main issue is trying to get some solid booking due to the Holiday. Otherwise, I'd take a chance and buy the ticket at the station.

No matter, how hard you both are trying to help me, I ended up at a dead end as soon as I decide to book the ticket. Why I keep getting the message " Since you are originating your trip in Norther Ireland you have to go to Translink period. No other choice? I got to that site and its horrible site to navigate.

I just got a link to LUas. But people assume that you are familiar. I don't have a clue there are two lines green and red. I don't have a clue which one. I was told early during my search that Luas was included on the train ticket from Belfast. Apparently that's not the case.

Believe me I have done my share of International travel and I have never ever encountered this type of challenge

Bus is also option for Dublin to Galway 
3/17  11:30 am arrives Galway 14:50 cost  15.20 euro 
The good thing about the bus is if it gets crowded they add additional bus 
 

Please only use IrishRail site and make a return ticket ( round trip)  for Dublin /Belfast  You will not have to deal with
Northern Ireland train site at all .