Dug a trench for a French drain. How should I move forward?

http://imgur.com/a/Y0Rx6

[California] I'm doing this on my own and I've never done anything like this before. When it rains, water flows to the piece of land to the left of the pathway and makes the area very muddy.

I dug a trench for a French drain along the pathway. The lowest end of the trench is about 14" deep whereas the rest is 10-7" deep. There is a tree about 5' away from the low end. I didn't dig any further because I was hitting roots.

What I plan on doing next:

1. Put down landscape fabric
2. Add some rocks to the bottom of the trench
3. Use steaks, string, and a line level to figure out how much higher/lower the rocks should be to have 1% slope (1/8 per foot)
4. Put in a perforated 4" drain

I don't know what comes next. Does the above look correct?

I have a bunch of questions:

1. How big do the rocks need to be? Do I use them to fill the entire trench or does something else go on top of that?

2. How exactly do I do #3 from above? Visual aids please!

3. Would I pipe like this work? Along with this?

4. Do I need to add fittings to either end of the pipe? What kind?