There is free parking and access to the park at the purple "P" parking lot (to the right of the "Difficult Run" label), which is about 3.5 miles west of the Beltway on 193 (Georgetown Pike), and one-half mile east of the intersection of 193 and Old Dominion Drive (738).
The red trail is the Fairfax Cross County Trail -- it connects the parking lot to the Difficult Run Trail going toward the Potomac River, where it connects to the Potomac Heritage Trail, which follows the Ridge Trail and River Trail north along the Potomac River through Riverbend Park, the Seneca Tract and onward into Loudon County. The purple trail is a faint, informal trail that climbs steeply along the west side of an abandoned quarry pit. The light blue trail starts across the road from the parking lot entrance. Here is a larger version of this map that shows trails to the north leading to Great Falls and beyond (but without the red, blue, and purple trails marked on the map below).