Itinerary with trains and ferrys from Milan to Lake Como and Bellagio

The search function here isn't great, but the question has been asked several times recently.
For Bellaggio, the most convenient way is to take the train from Milano Centrale to Varenna Esino, then the frequent ferry from Varenna to Bellaggio.

• The east side of the lake (including Varenna) has a rail line, running from Milan to Tirano, which is on the Swiss border and connects with the Bernina Line into Switzerland.
• Como town (south-west end of the lake) has a station on the main rail line from Milan to Switzerland via Lugano.
• Menaggio has a bus service from Lugano.
• Otherwise it is lake ferries or boats.

To the excellent summary of Chris, I would add the commuter railway line from Milan (Cadorna station) to Como Lago, a tiny station just crossing the street from the ferry pier, that has its utility if you want to try a circular itinerary such:
train Milan (Centrale) to Varenna
Ferry Varenna to Bellagio
Ferry (much more scenic) or bus Bellagio to Como
Train Como Lago to Milan (Cadorna)

(or the other way round)

I think the best day trip option is to take the train from Milano to Varenna (about one hour). From there you can get a 'mid lake pass' for the ferry and easily visit Bellagio as well as several other (too many for a day trip) villages. The trip from the town of Como on the ferry is pretty, but not as pretty as the area in the mid lake region and takes a few hours and by taking the train up to Varenna and then ferry around (and then the train back) you maximize your time.