Seeking travel advice

https://www.italiarail.com/pages/routes/rome-to-assisi

Use trenitalia to purchase.
https://www.trenitalia.com/en.html

Assisi is great and it the Umbria region. Suggest visiting Spoleto, Gubbio, Perugia and Orvieto as well.

Hi, Giangilberto from Milan, well, first of all, it depends on which airport you are using: Fiumicino is a major intercontinental hub—one of the most important in Italy, if not the most important,whereas Ciampino is smaller and primarily serves low-cost airlines.
All trains from Rome to Assisi depart from Termini Station, so your first step is to get there; from there, you can continue your journey to Assisi.
From Ciampino, there is the "Ciampino Air Link",a Trenitalia service that takes you to Termini. Here is the information from the official website:

https://www.trenitalia.com/it/regionale/collegamenti-regionale/ciampino-airlink.html

Choose Ciampino Airlink, the train-plus-bus service that connects central Rome with Ciampino G.B. Pastine Airport quickly for just €2.70.
Conveniently located just a few meters from the airport entrance, the bus service takes you,non-stop and in just 10 minutes,to Ciampino Station, where you can continue your journey to Rome Termini.
Ciampino Station also offers frequent connections to other destinations in the Lazio region, such as the Castelli Romani area and towns in the Frosinone province.
Where the Link bus departs from:
At the airport, the bus leaves from the forecourt in front of the terminal (at bay no. 6). At Ciampino Station, the bus departs from right outside the station exit (on the Platform 1 side).
You can view all travel options and purchase the combined train-and-bus ticket on this website or through any of our sales channels by selecting "Ciampino Aeroporto" as your origin or destination. You can use the Leonardo Express from Fiumicino; here is the official information from the Trenitalia website:

https://www.trenitalia.com/it/regionale/collegamenti-regionale/leonardo-express.html

I had to split the reply into two parts because it exceeded the character limit allowed by the forum for replies.

The Leonardo Express is the non-stop service connecting Roma Termini station to Rome Fiumicino Airport in just 32 minutes.
The service runs every 15 minutes*:
from Roma Termini between 4:50 AM and 11:05 PM
from Fiumicino Airport between 5:38 AM and 11:27 PM.
The train station is located inside the airport and is easily accessible.
Ticket price: only 14 euros! If traveling in a group, the "Minigruppi" fare allows you to purchase 4 tickets in a single transaction for 40 euros instead of 56!
You can also purchase a 10-ticket pack (single trips) for the great price of 115 euros.
X-GO members who purchase Leonardo Express tickets earn 2 points for every euro spent, these points can be converted into cashback to use on future trips! If you haven't joined the X-GO Program yet, click here.
To travel on the Leonardo Express, you can use the new TAP&TAP quick-purchase option: simply tap your contactless payment card, smartphone, or smartwatch on the readers near the departure platforms, and with a single tap, you can board the non-stop train between Roma Termini station and Fiumicino Airport (or vice versa).
Remember, if you choose the Leonardo Express:
children under 4 years of age travel for free;
for every paying adult, one child between the ages of 4 and 11 (up to their 12th birthday) travels for free, You can bring along,at no extra cost, a small dog (provided you have its canine registry certificate), a cat, or other small pets in a suitable carrier;
luggage, even large items, is not subject to a surcharge.
All Leonardo express trains feature designated seating and restrooms equipped for passengers with reduced mobility, and guide dogs travel for free.
Metrebus integrated tickets are NOT valid on Leonardo express trains.
Once you arrive at Rome Termini station, you can take a train to Assisi; there are various options. In my view, the best ones involve regional trains: some require a transfer, with a total travel time ranging from two and a half hours to just under three hours, while direct trains get you there in a little over two hours.
You can find all the rules regarding regional tickets at the following official link:

https://www.trenitalia.com/en/information/travelling-on-regional-trains.html

Assuming you are referring to FCO- to simplify-

Trenitalia
https://www.trenitalia.com/en.html

(Italiarail linked above is a third party reseller- use the official train site- Trenitalia)

Take the Leonardo Express to Roma Termini then transfer to a regional train to Assisi.
The Assisi station is outside of town, bottom of the hill. A bus will take you up to town.

Regional trains do not need to be purchased in advance as the price never changes and they can't sell out.
iI you are flying in to FCO this day then it is best not to purchase in advance in case of delays, etc- just get the tickets once you are thru passport control and have your bags.
Get the easy to use Trenitalia app or buy tickets at a kiosk.

Thanks everyone for the suggestions. I am flying to FCO airport and going to Assisi, stay 2 nights there, I have 2 more days, planning to visit the nearby towns and fly back to FCO.