how to dress in early april?

Italy is huge and has temperature variances - there is no single average country temperature, it's city-specific. Type into Google the city you're interested in + monthly temperature averages, as in "Rome average monthly temperatures" or "Rome April temperatures"

It is hard to predict the weather. I have gone in May and worn everything from sweaters to shorts. I doubt you will need a coat. Bring things that can be layered easily and removed when you are warm.

It would help to know where in Italy, North or South. Here is a link to Weather Underground,http://www.wunderground.com, put in your location and select. You can go back in years and see what the temp was for that area on a specific date.

You need to be more specific on where you are going. Italy is very long north to south. Northern Italy is located at the same latitude as Washington State. Southern Italy is at the same latitude as Northern California. Weather will also vary depending on altitude and the Alps are 10,000 to 15,000 ft high.

It's also impossible to predict so far in advance. Check the weather forecast on Wunderground.com just before you go.

For now I can give you the averages for April in some sample cities:
http://www.holiday-weather.com/rome/averages/
http://www.holiday-weather.com/florence/averages/
http://www.holiday-weather.com/venice/averages/

As you can see in April the temperatures in those cities are around low-mid 60s F during the day while at night they might drop to the high 40's-low 50's. A heavy coat might be too much unless you go up in altitude, but a sweater only is probably not enough in the evenings. Sweater + Jacket is what I generally wore in Florence in early April when I lived there.

It depends on where, as others have said. If you are used to cold winters, Italy in April will not feel cold per se. But it may be cool. Unless high in the Alps, you will not need a winter coat. If it's 50s, which seems likely, I have had my kids layer a t-shirt (long or short sleeve), a hooded sweatshirt, and a light windbreaker/rain type jacket. All pieces can be used as needed (sweatshirt is good for cool nights even if it's hot during the day, light rain jacket is good for rain in any temperature) and layered for fairly cool temps. Lighter weight than bringing a heavier coat, too.

I'd check the weather for your cities a month out (see if they are in some weird hot or cold wave), then check the forecast frequently as time goes by.

There is a good possibility of rain during that time period so rain jackets are necessary. Two years ago we were in Tuscany in mid-May. It was cool and rainy. Not hard. Just a little sprinkle or a bit more nearly daily. Quickly followed by the sun but we wore long sleeves and jackets each day. It was not short weather. I would assume that the first week of April would tend to be cool if not pretty cool and rainy.