I usually park on Manitou avenue just short of the start line. If you go beyond city hall, there is a 3-hour time limit and you will get a ticket. It is best to begin at the start line so you get a better idea about your total time. Note: the Ascent joins the Barr Trail after the first aide station. See the COURSE on this website.
The Cog RR runs trains every 80 minutes. Once you get to the top check with the conductor for each car if they have any vacant seats. The price is $20. I have found the odds are about 50-50 of having a seat. You can generally get a ride with the tourists or even other runners, but you have to ask. Most people will have a hard time believing you hiked all the way to the top. It is also a nice gesture to compensate them for the ride.