Perhaps the easiest and most convenient way to travel to Bagan is by Air. All local airlines have daily flights to Bagan. Some airlilnes run more than one flight a day. These flights usually follow the rout Yangon-Bagan-Mandalay-Hehe-Yangon (or in the opposite direction). Thus it is convenient to plan your trip along these destinations. Air far is usually around US$ 80 – 100, one way, depending on season. For details on airlines, please see the article Domestic Air Travel Advice.
From Bagan (Nyaung Oo) Airport, you can take a taxi to Nyaung Oo town or Bagan. One point to remind you is, if you include Mandalay in your trip schedule, Mandalay Airport is outside the town and about one hour drive from the city. And taxi to and from Mandalay Airport is quite expensive.
If you are on budget, then the best way to travel to Bagan is by bus. From Yangon, all buses leave at around 3 PM, and arrive to Bagan the next morning around 5 AM. The Bagan bus terminal is inside Nyaung Oo, just at the base of Shwe Zi Gone Pagoda. From there, you can take a trishaw, a horse cart or just walk to your hotel/guest house. For details, see the article Bagan by bus from Yangon.
From Mandalay, it is a different thing. Buses from Mandalay leave in the morning, take the whole day, and arrive to Bagan in the afternoon or early evening. The arrival schedule is not very precise. The buses are not air-conditioned buses, and usually carry a lot of luggages, slow, hot and overcrowded. It is better to avoid using bus from Mandalay to Bagan, unless you want to experience local way of travel.
There are a few overnight buses from Taung Gyi (Shan State) to Bagan, but they are very slow, very crowded and carry a lot of luggages under the seat.
You can get bus schedules to Bagan and to other destinations at the following website with bus fares: Bus schedule in Myanmar.
The most convenient way to travel from Mandalay to Bagan is by boat. This is my favorite way to travel from Mandalay to Bagan. the boat usually leaves around 5 AM in the morning from Mandalay and arrives to Bagan at around 3 PM in the afternoon. The boat trip is smooth and you can sleep on the way, and refill your energy which you will need while your stay in Bagan. The boat will cost around US$ 20 per person. You can have your breakfast and lunch on the boat.
This is the least recommended way of travel. Slow, dangerous, overcrowded. Just see the article To All the visitors to Bagan who would travel by train. If you still insist on travelling by this rout, trains leave everyday from Mandalay, and arrive to Bagan the next day. The train station is just outside Nyaung Oo town, and you can take a taxi, trishaw or a horse cart from Bagan Nyaung Oo Railway station to Nyaung Oo.