Sörmlandsleden is one of the bigger trails in the Stockholm area. It is well marked and can be accessed by commuter traffic and can therefor be walked from A to B. It starts at a subway station called Björkhagen The trail has windbreaks in the camping areas which most of are situated by a lake with drinkable water (boil or filter if you want to be sure). The homepage has alot of information and maps for members. The trail is well marked and water sources is scattered all over so you don’t really need more guiding.
This map contains the actual hike and camping areas and water sources.