The best way to get to Carthage and Sidi Bou Said is by taking the small suburban train known as the TGM. It travels from the Tunis Marine TGM station at the eastern end of Ave Habib Bourguiba and passes through La Goulette, Carthage and Sid Bou Said before ending at La Marsa. Second class costs about 650 mills and can be quite crowded whilst first class costs TD1.1. The journey to Carthage takes about 30 minutes.
According to my copy of Lonely Planet Tunisia, "...you will need near superhuman stamina..." to cover all the sights that Carthage has to offer. Although the sights are very spread out, you can visit them fairly easily in one day but, be warned, you will have to walk a fair distance between them to achieve this (about 6km/4 miles). Now, I'm not the fittest guy on the planet and even I managed it and I would hardly call myself "superhuman". I spent quite some time at each one so I wasn't rushing around either. Visit one of my travelogues for more information.
Carthage is very easy to reach from Tunis. Regular trains leave from the Tunis Marine TGM station in the Ville Nouvelle and stop at all 6 stations in Carthage. The ruins are spread out over a large area in Carthage. Carthage Dermach or Hannibal are probably the most convenient as they are in the centre near the museum and the majority of the ruins.
The journey took about 25 minutes from Tunis and tickets in second class cost a mere 1.6 Dh. The train can get quite crowded and it's difficult to get a seat, especially in 2nd class so it might be an idea to buy a 1st class ticket, which doesn't cost very much more.
The best way to reach Carthage if you are staying in Tunis is to take the TGM (suburb train line). The 30-minute ride from Tunis Marine station to Carthage costs approximately 1 dinar.
There are 6 stops in Carthage, but the one closest to the most attractions is Carthage Hannibal (the 4th one). It is also good to know that Byrsa Hill is nearest to the Carthage Hannibal station, NOT Carthage Byrsa.
There are train services from approximately 5 a.m. to midnight. Try to avoid the rush hour, since the trains can get pretty full at this time. The frequency of departures varies according to the time of day.
On a side note, Carthage's attractions are located just far enough from each other to make walking impractical (that is, if you intend on seeing them all in one day), it is recommended to take the occasional taxi to get around. I guess biking would also be a great alternative, but I have no bike rental shops to recommend.
The TGM is a suburb train which goes from Tunis to the northern suburbs of the city. It runs every 15 minutes from a station which is a few 100 meters away from the main train station (you may take the tram or a taxi, but we decided to walk). This station called Tunis Marine is situated at the eastern end of the Avenue Habib Bourgiba.
For the archeological sites of Carhage, I would recommend to get out at the station of Carthage / Salambo. It is close to the Tophet and within walking distance of some other sights.
that's the bus that drove me to carthage amazing roman ruins. a wonderfull place to snapshot at will and bring a lot of memories.of course yu can hire a car and drive there, tunisia is a very small country and the roads are good and with enough road signs...but taken an excursion it is safe enough and very pleasent.
To reach Sidi Bou Said from the capital Tunis, the easiest way is to rent a taxi for an afternoon. It will bring you stra8 to the village, or you can mix and organize an excursion like this.
You leave Tunis and visit all the sites of Carthage, then the taxi will take you to Sidi Bou Said and then back to the capital Tunis.
The cost of all this should be around 50/60 Dinars, so pretty acceptable.