Rome was famously "not built in a day" but you can make a good tour of it in eight hours. Coming from Tuscany and Umbria, most will arrive at the main rail station "Termini".
There is a choice of following our routing, given below, for which you will have to travel by metro, bus and/or taxi and do a bit of walking or simply buy a ticket for the red tour bus. This open topped bus, travels a route around Rome that passes or goes close to most of the places you will want to see in a day. There are buses every fifteen minutes and the ticket (€15) entitles you to get on and off as many times as like. If you do this, make sure you get off the bus to see the Piazza Navone, Parthenon, Piazza di Spagna, Trevi fountains at the very least as the bus can't get to them.

You buy the ticket in the bus station outside the rail station - the ticket office is on island E and  the red buses stop on the far right of the bus station as you look from the rail station. There are also special bus tours starting here for "Christian Rome".  DO NOT take the alternative circular bus tour run by CLT - they are unreliable.

The Gorgacce Rentals Tour
The route we take with our friends.
Take early train, about 06.50,  from Terontola arriving Rome about ) 08.30  (There is a later train at 08.11 but it takes longer to get to Rome and may mean curtailing the tour a little.)
Proceed to metro- directly below the main station and buy a book of tickets that can be used on metro and buses (at least three per person). (You can buy them near the metro and they are also on sale at tabacchi shops (the ones with a big "T" sign) You are expected to cancel each ticket yourself - at the station before you start a journey ("validita") and on the bus.
Metro to Ottaviano - walk to Vatican museum (closed Mondays). Its four to five hundred metres. Buy ticket and make way to Sistine chapel. Resist temptation to look at anything else though we usually stop in the medievel maps room.
Walk round Vatican walls to St Peter's square (can send a postcard with Vatican postage stamp). On Wednsday mornings the Pope has a public audience in the piazza (Dilys was once asked by a tourist - "who's that man in white") Bus 64 (possibly other numbers too) from Piazza San Pietro to half way down Corso Vittorio Emmanuele, if possible get off at the Museo di Roma (the bus crosses the Tiber and does a one way circuit before driving down the Corso V.E. get off at the 2nd stop, Museo di Roma);  or take taxi - to Piazza Navone (square with three fountains).