transportation

My first stop on our Italy trip will be Varenna and we are flying into Milan. There is a train on Trenitalia that stops in Varenna and you can get it from Milan. You can use the trenitalia website to show you the schedule (there is a english version on the site). The trains also don't put a schedule far in advance on the site but from my research and other similar questions on there, the schedules are about the same time each day. If the date you are traveling is too far in advance on the website, just put the day of the week you are traveling to see the times. For instance if you know you are traveling on a monday, use next monday date to see the possible schedule. My trip is in september and that is what I'm doing to see the possible schedules from city to city.

Train to Varenna from Milan:
www.trenitalia.com To Limone, go back to Milan, then train to Desenzano (on the Milan/Venice line). From Desenzano the best way, although not the fastest, is by boat (you'll enjoy the beautiful views on the way there). Otherwise bus from Desenzano to Limone.

I went on the trenitalia website and could not find a train from milan to varenna. I did find a train to como. Maybe you have to take a ferry to varenna. If you have another train system please let me know.
Do you know what bus transportation there is from milan to varenna?

There are plenty of trains from Milano to Varenna. You might have looked at a date too far ahead. Just check the schedule for any day next week, it won't change much in summer.