Ive never traveled outside of the US before, and Im in search of affordable accomodations. Also, does anyone know what are standard fares for taxi's in dublin?

Globetrotter's Tourist Hostel (gtrotter@indigo.ie) and Mount Eccles Court (info@ecclescourt.com) are 2 nice & cheap places to stay. Taxis are expensive. I can't give you the exact rate, but there are good buses and a new light rail system. You can also rent a bike.

Well it depends where you want to go.
One thing is that in Ireland, you tend to find a LOT more bed and breakfasts than hotels. And most of the bed and breakfasts they have are very nice.
Generally the smaller B&Bs are much more comfortable, and the price is only slightly higher.

If you are traveling to the Southwest, I'd suggest staying at Kenmare B&Bs.
If you are traveling to the West Coast, stay at Connemara B&Bs.
As far as the Southeast goes, maybe Waterford Bed and Breakfast.
Wicklow is a nice Bed and Breakfast on the East Coast.
I don't know of any GOOD bed and breakfasts in the midland, so I'd suggest staying in a hotel. For me the hotel experiences were all the same so just go for what's affordable. Never been to Northern Ireland so can't help you too much there.

Great accommodation deals at the moment all over Ireland - most have been reduced to pre 2005 rates.
Enjoy the savings.