The Joplin Trail begins in the foothills above Trabuco Creek, climbing the canyon between Modjeska and Santiago Peaks before connecting with Main Divide Road. From here, one can easily make their way to either Modjeska or Santiago via Main Divide Road, or by the shorter use trails. The trail is very steep and runs through very densely wooded areas. The trail is often used by mountain bikers descending from Main Divide Road; keep your ears open and it shouldn't be an issue.
(See Directions on the Holy Jim Trail page if you need to find out how to get to Trabuco Creek Road.)
As far as I know, the only ways to access the trail without trespassing are Trabuco Creek Road or the Santiago Truck Trail (a much farther option). To get to the trail via Trabuco Creek, follow the road about 1.8 miles from its start (~half a mile past the Trabuco Flyers Airstrip) to the huge turnout on the left side of the road (33.671663, -117.559187). There are various turnouts in the area to park on. You can alternatively park at the turnout where the road starts if you don't want to drive your car on the dirt road.
From the turnout, climb the steep, rutted road. At about 0.7 miles, take the right fork at the first junction (33.675230, -117.562537). After about 1.1 miles take the right fork at the second junction (the narrower trail at 33.684284, -117.563269). Travel about 1.5 miles under the power lines on this relatively flat section. At the next junction, follow the trail down to the left a little less than a mile down to Old Camp (33.694712, -117.549913, the right trail goes up Power Line Ridge). After passing through Old Camp, climb 2.6 steep miles through the forest to reach Main Divide Road (33.717239, -117.540121). Make a right on Main Divide and just around the corner you will arrive at a clearing (33.717509, -117.538788). Here you, will find use trails to access Santiago or Modjeska.
Long sleeves/pants (poison oak) and a walking staff or trecking poles. Lots of water. Seasonal water can be found on the trail at Old Camp and a few spots further up.