I have only picked up a few of the little tricks from watching, but I'll try and help as best I can.
Pouring and getting the right height is easy if you set the top of the forms so that you can run a board along to level it off. Then we run over it with wood floats to bring up the moisture and knock the rocks down. It then got hit with a 3 foot bull float to bring up more moisture and show if anything isn't level or smooth. After it sat for 30 minutes or so it got hit again with a steel float several times. At this point it was about 2 hours after the pour and you can feel it starting to set up. Each time it got hit with the steel float, the marks were becoming smaller and smaller. The finish on this porch was started about 3 hours after the pour and was done with a soft bristle push broom. It has to be done right when the concrete is almost done setting up. You just gently drag the broom over with nothing, but its own weight on the concrete. If you wait too long then you lose it, if you do it too soon then it makes a mess.
You also have to do the edges during this whole process. You hold a small trowel at an angle and run it over the face of the concrete to push the rocks back. This is what gives a nice smooth edge like you see on the end of a garage. You also have to use a rounded edger tool to give it a nice round edge on the corner.
I hope that doesn't scare you too much. It's always messy and you always rush around and then stand there watching it harden. There's a lot too it, but nothing that difficult once you have seen it done a few times. I would recommend helping someone do it a couple of times. They will appreciate the help and you'll learn something new. Like everything else though, the professionals make it look easy.
Edit: Here's pictures from today with it all nice and dry.
