If you decide not to rent your own car it is very easy getting to Trim. The best and most economic way is by bus, as taxis from Dublin and Dublin Airport can be very expensive. You can use the Bus Éireann service right from Dublin Airport. You'll need to change buses in the Busáras terminal in Dublin City Center, but it is fairly painless. The route that takes you to Trim is #111 and tickets are VERY AFFORDABLE. The buses are clean, comfortable, but make sure you sit closer to the front- as again -the roads in Ireland tend to be winding and hilly. And some of those bus drivers like to take those roads like they're at the Brickyard 400.
Trim is a small enough town to where you can walk to wherever you need to go, and there are plenty of signs directing you to everywhere you'll want to see and do. Depending on where you're staying, you may need to use one of the taxi firms that operate in Trim just to get into the center of town, but once there walking is the best way to explore the town, the attractions, etc. It will really help to appreciate the town.
If you can get a hold of a bicycle, that would be perfect. You then may be able to use that to get to and from the town and definitely get around much quicker. But if you do, you'll also need to buy or borrow a reflector vest as it's the law in Ireland to wear one whilst riding bicycles. If you cannot get a hold of a bicycle it might also be worth it for you to buy a bicycle while you're there. You can take it with you if you're traveling Ireland by bus or by train. It's a great way to get around without blurring past everything in a car. And when you're done with the bike you can give it to some kid and become a hero : )
I've noticed that car rentals have become much more affordable these days than in years passed. Almost all of the major car rental companies have moved into Ireland, creating a lot of competition. The benefit of renting a car, of course, is being able to travel where and when you want to. But make sure you're able to handle the totally different style and system of driving as many of us know it in places like the US and Canada. Driving takes place of the left side of the road and the driver sits at the right side of the car.
Driving to Trim from Dublin is simple. If you're driving in from the Airport you'll need to take the M1 to the M50 and then the N3 and follow the signs.