You can't really run through the slot canyon, it can get pretty narrow. Plus if there are people in front of you, you won't be able to run past them. You'll have to wait for it to open up to go around them. There are ladders as well, which will definitely slow you down.
Getting here is really easy and straight forward. You can google "Ladder Canyon Trail" and google maps will literally guide you to the trailhead. Once you get close, the road becomes unpaved and there is a sign that says 4WD vehicles only. This is misleading as the road is very well maintained and easy to navigate. I did this in my 2-door sports car that is low to the ground and I had no issues going fast enough to pass SUV's going slow.
The Ladder Canyon Trail is an exciting trail. The first time I went here I was just wowed every time I came up to another ladder. The running itself is not difficult at all. There are a few parts where you might get turned around, but every time I came to a point like this, there was an indicator (usually a pile of rocks made into an arrow) that points you in the right direction. Weaving through the slot canyon is really beautiful. You get to see things that just aren't common around Southern California and are mostly found in places like Utah.
The beginning of the trail is kind of hard to find your first time here. I only found it because I happened to see a couple go off into an area I wouldn't have gone without knowing that that was where the Ladder Trail started. There are indicators though through this entire canyon if you are paying attention, and a sign marks the trailhead. I wasn't aware of this until later. There are also rocks piled into arrows that indicate the direction you should take when you come to a multi-directional fork.
This trail ends at the Painted Canyon Trail
that follows a different route back to the car. Once it ends you can continue on that trail, or turn around and take the Ladder Canyon Trail back. You would simply be climbing down ladders instead. When I did this I took the other trail back simply because I had never been here before and wanted to see it all.
The other trail is more of a "Make your way through a big canyon" kind of run. Huge walls of rock (this place is killer if you are a geologist) and lots of minerals and rocks line the trail. It is a bit more exposed since you aren't in the slot canyon anymore, so again be safe out there in the sun.