Good luck, reis! I've done the CN Tower stair climb 3 times, and
posted about it in 2005. I think my best time was about 22 mintues.
As for training, just practice climbing stairs. Some of the taller hotels in Toronto (like the Sheraton--I entered from the lower convention level, then took the elevator down) have stairwells that you can enter publicly (be careful of office towers, as the doors that lead to the office floors may require a pass key; hotels don't seem to have as much security, either).
On the day of the climb, try to go earlier rather than later, as it gets more crowded later in the morning. With so many people of varying ages and fitness levels (from kids having to be carried by their parents, to girls chit chatting), if you want to climb quickly you want to go when there are less people clogging up the stairwell--which is relatively narrow (I could stand in the middle of the stairs and reach the railing on either side--this is helpful when you are tired and need help finishing--although obviously if there are people coming up behind you you need to keep to the side).
There are paramedics at selected floors, and you can rest on any landing if you are tired. Some people will sit on the stairs to rest--getting in everybody's way. Keep to the side, people!
It's fairly cool in the stairway. They've changed the rules (for security reasons) on what you can bring(bottled water or not), so check before you take anything with you. Good luck!