Having had the experience of going through the locks at both ends of the Canal, IMHO the best way to see it is at the Miraflores visitors' center. You'll have a much better vantage point and you'll be better informed and entertained. The museum is well worth seeing. Plan on spending a couple of hours at the center.
I'd also recommend that you get there early in the morning. Traffic on the Canal usually ceases between 10 and 11 am. That's because they change the direction of the ships in the Canal. It doesn't resume until 3 or 4 pm.
The best way of getting to Miraflores is by taxi. However, don't grab a cab at your hotel, where you'll be told that the fare is $15. Instead, walk across the street and catch a taxi at the curb. The cost from El Cangrejo will be $7. (If it's raining, forget cheap fares for taxis ... if you can find one.)
If you want to see the Canal, I wouldn't recommend taking the train. You'll see very little of the actual Canal. Once you get to Colón, you should hire a taxi for the day and get out of town. Colón is not a safe place for tourists or Panamaños. There are some interesting sites within the province, such as Gatun locks, Fort San Lorenzo and Portobelo. Portobelo is an hour away from Colón, and it offers a nice look at Panama's colonial past. You can hire a tourist taxi to see Portobelo for around $60 per person. Hiring a taxi to take you back to Panama City will cost between $75 and $100.
However, with only one day to see Panama, I would suggest something more like this: Spend the morning at Miraflores. Take a taxi to Casco Viejo (the older part of Panama City) for $10. Have lunch at the nearby Mercado de Mariscos (Fish Market) or at one of the many restaurants in Casco Viejo. Then, do a walking tour of Casco Viejo. If you like history, check out the Panama Canal Museum.
I hope this is helpful.