Rome to Capri

Depends on what time of year but "fast" train to Napoli Centrale, taxi or bus transport to the port and then ferry to the island is the most direct way. With a small child, I wouldn't take the Circumvesuviana commuter train from Naples to Sorrento and then a ferry from there.

https://www.capri.net/en/ferry-schedule

I don't disagree with the first answer, but nothing in Italy is "simple". One issue is the date of travel. The footnote in the link provided (which says "Starting April 30") says:

"The schedules change often; the times on this page refer to the current week. Check times again shortly before your travel dates.
In case of rough seas: before departure, we suggest you contact the ferry company by telephone (see number in the sidebar) or call the Capri information office."

When you look at the PDF, you learn that there are multiple companies that offer the service. Each will try to get you to buy a round-trip ticket, and won't tell you about the competition's hours or size or comfort. The ferry home may leave from a different slip, up to 1/4 mile away from the slip you arrived at in Capri.

You also need to know that the Frecciarossa trains from Rome are much cheaper three months in advance, and are non-changeable, non-refundable tickets at the discount prices.

You asked a perfectly reasonable question, but it was a very spare inquiry. You might get the best advice if you mentioned not only the month of the year and the number of people, but your plans in Capri, whether this is a multi-day trip, where else you want to go in the area (Pompeii? Sorrento?), and the volume of luggage you will have. Are you sleeping on Capri? Are you going to the Blue Grotto? Will you have a fold-up stroller (pram)? (Distances are huge on Capri.)

With your trip being next week and so little detail, it will be a challenge for the forum to give you useful info that you can implement in time.

Looking at your other post, it's tough to tell whether you are staying in Rome for the duration of your trip or are also staying in other locations, such as Capri, as well? I will caution that Capri isn't really a day trip from Rome: it's too far and frankly too expensive, when all the transport costs are added up, unless planning to stay a night or two.

I hope you're not planning on doing this as a day trip, especially with a four year old. Could you clarify your situation?