It sounds like the best way to Bellagio is to take the train from Milan to Varenna-should I purchase tickets ahead of time or is that a frequently run trip and not neccessary?

Not necessary to buy ahead IMO.

Trains run from Centrale about every two hours. The actual station name is Varenna-Esino. Trains have mostly Second Class cars...on this equipment First Class really isn't worth the extra money.

Trip takes a little less than 1.5 hours.
Sit on the left hand side of the train (facing forward) for the best lake views which begin at Lecco.

Taxis usually meet all the trains arriving from Milan. The ferry dock is about a 10-15 minute walk, all downhill, from the RR station. Buy your tickets at the booth there.

Ferry to Bellagio takes about 10-15 minutes; some are direct and some may stop in Menaggio first.

If you plan on leaving Lake Como by train, be aware that you can't buy train tickets at the Varenna train station. There are a couple of places in town that sell tickets, but you'll want to make sure they are open when you want to buy your tickets. If you know when you are leaving, you can go ahead and buy your tickets to and from Varenna before you leave Milan.

Great advice from Intrepid - we just did this trip a few weeks ago.

Only thing is, we did not see any taxis meeting our train when we arrived at Varenna...the walk to the ferry wasn't bad though - though I can imagine it would be quite rough with a lot of luggage (we only had carry-ons).

We were on a mid-day train on a Tuesday, and had our car almost to ourselves.

Our friends took the train to Varenna and it worked out....although it was late, they couldn't get the ferry to Bellagio and spent the night at the last minute in Varenna. (a lovely place)
My husband and I took the train from Milan Central Station to Como (spent the night because we wanted to see Como) and then took the Hydrofoil the next morning straight to Bellagio. Worked out great and the ride up lake Como on the hydrofoil was gorgeous with the villages, villas, etc on the side hills.

Thanks to all for the advice. It is easier to know these things ahead of time instead of figuring them out yourself when you arrive.

As others have mentioned, it's worth buying return ticket in Milan so you don't have to worry about finding a place to buy them on return -- they don't have to specify which train but don't forget to validate the ticket in the yellow machine before you board.

We tried to follow Intrepid's suggestion re: which side to sit on, and yes, the left side (going north) has the best lake views, but both sides have some lovely mountain views, and the left side also gets direct sun after noon, which can get quite warm (and, obviously, the right side southbound gets the same afternoon sun).

Seems to me the last ferry is somewhere around 10 pm and there didn't seem to be too many taxis around, esp. for that arduous (albeit short) trip UP the hill from the Bellagio ferry to the train station on the way back.