Book on Trenitalia; the Rome to Assisi line is regional, so there is no high-speed option and tickets are bought by day, not by seat. The first morning departures put you in Assisi mid-morning and the last useful return leaves in the early evening, so plan on reaching the Basilica of St. Francis by late morning and leaving the old town by about 6:00 p.m. From the station a city bus runs up to the old town, covered on how-do-i-get-from-assisi-railway-station-to-the-old-town; the Porziuncola is a short walk from the station, which makes it the natural first or last stop.
The basilica's lower church opens 6:00 a.m. to 7:00 p.m. (6:00 p.m. on Wednesday), the upper church 8:30 a.m. to 6:45 p.m., and the tomb crypt 6:00 a.m. to 6:15 p.m., with Mass in the lower church at 7:15, 10:00, 11:00 and 6:00 p.m. on weekdays. The Porziuncola basilica is open 7:30 a.m. to 12:30 p.m. and 2:30 to 7:00 p.m. A day trip can cover the tomb of St. Francis, St. Clare, the Spogliazione shrine with Carlo Acutis's tomb and the Porziuncola, but not the Eremo delle Carceri or an unhurried Mass.
Strikes and line works on the Foligno to Terontola section are posted on Trenitalia's notices; check the day before. The wider question is on can-i-combine-rome-and-assisi-on-one-catholic-pilgrimage.