Hi, I'm just back from lake garda 2 weeks ago. We stayed close enough to Peschiera del Garda and I flew home from Milan Malpensa airport so I did this exact train ride!
Milan Centrale is a big railway station, there's around 15 train platforms, bus station outside and metro stop underground. I'm fairly confident getting around but I was very glad I did'nt have my neice with me when I was trying to get through here!
If you go here http://orario.trenitalia.com/b2c/npp...n&channel=tcom
I've retrieved the trains for that day leaving Milan Centrale (MI C.LE) to Peschiera del Garda. When you get to the train station there's 2 or 3 huge boards hung from the ceiling with the departing train information. For each train it will show the platform, departing time, and final destination. Intermediate destinations are scrolling alongside the train info so if your destination is not the final destination you will need to check the intermediates to see which train is actually yours.
I'm not sure if you can buy your tickets online and completely bypass the ticket booths. We tended to check the timetables online and then buy the ticket using the automated machines when at the station. The automated machines have an english option and hence are straightforward to use. I did see an option on them to collect internet tickets so you may need to buy online and then collect at the machine when you get there. There's plenty of these machines so you should'nt have to wait too long to use one.
As this station is very busy I would suggest parking your wife and children (I mean that in the nicest way possible!) and you go to get the tickets, check the platform etc, alot easier moving children and bags when you know where your going. A word of warning concerning Italy's public transport, its very good but if a train/ferry/bus arrives ahead of time it does not wait until the time stated on the timetable. So if your there ahead of time and your train is there, get on it!
I found the italians quite helpful when you had an idea what you were doing and always asked a local to confirm the train was going where I thought it was going. Give yourself plenty of time and you'll be fine, as far as I can see the train will go straight to Peschiera del Garda with no change-overs. On the boards you can count the stops before yours and it will show exact times of each stop aswell so there's lots of info you can gather to ensure you dont miss your stop or get off at the wrong one.
Best of luck and enjoy the trip. Lake Garda is beautiful def go to Gardaland, my niece(4) LOVED it