To go to Sour from Beyrouth you take a bus from Cola station to Saida. In Saida you change buses. They are frequent and the price depends on the kind of bus. Beyrouth - Saida costs between 750 LL and 1500 LL (June 2002), the same for Saida - Sour.
If you travel from Beirut, you have to change minibus at Sidon. The distance is arounf 45 mins from Beirut to Sidon and another 45 minutes from Sidon to Tyre. Both minibus rides cost 1,000LL (Nov 04). If you want to do a day trip, you had better go to Tyre first and Sidon in the return leg. When I travelled back from Tyre to Sidon, the minibus used the costal road instead of the highway. The distance is a bit longer but you can see different things.
To get to Tyre from Beirut it's best to look for a service minibus from Cola Station - a large crossroad in the city. They let you off by the old port in Tyre, right n the old city, and about only 10 minutes walk from area one.
. I hear that there are also buses leaving from Charles Helou, but I did not try them first hand. We asked about private taxis: 30 dollars one way - which isn't too bad if there's 4 of you sharing one.