As with any sport, warming up for Freediving is an essential part of a successful day in the water. I'm sure that any seasoned freediver will attest that as the day goes on they dive better and better. With a proper warmup, you can speed that up and reach that "perfect dive" more quickly. So what do I recommend? Well first, let's look at what the average freediver does before he makes his first few dives.
The average diver (and I used to be one as well) suits up, jumps in the water and does a couple of quick dives to 20 or 30 feet and tries to hold his/her breath as long as possible. Then they grab the speargun and take off after that first fish or grab the camera and start chasing a turtle. Sound about right?
I suggest starting you warm up first thing in the morning before you even leave the house. Start with some stretches. Do some limbering up with some simple stretching and then do a few inflated lung side bends (streches). Then sit down, get your breathing under control (diaphragmatic breathing) for 2-3 minutes and then do a few diaphram stretches with empty lungs. I then lie down, again focused on breathing, and begin a breath-hold table with 5-8 reps. Once I'm done with my breath holds I spend another couple of minutes just breathing and relaxing; it feels good and it's always nice to finish with a "good" experience. Then I get my breakfast and get my gear together.
Once I'm at the boat and we are heading out I try to again sit and breath for several minutes. This helps to get that relaxed feeling back. It also tells my body what to expect which helps speed up the Mammalian dive reflex. I also make sure I'm slowing everything down. I slow my movements, lower my voice, and generally try to take it easy. This is what I call slowing my mind; I'm trying to get into that "zen" place even though I'm being sociable and productive.
Once I'm in the water I spend the first few minutes simply getting my breathing right. If my breathing is correct, my body will do the rest. I usually begin with facial immersion and breath out of my snorkel for about 3 minutes with my face in the water. Although some professional freedivers poo-poo facial immersion, I do it because it's part of my routine and it seems to help me relax.
Whenever possible I do a few pull downs to kick in the dive reflex. If we've dropped the anchor I usually use the anchor line. Other times we will have a weighted drop line and I'll use that.
If no line is available, I usually do a dive to 30 or 40 feet and stay at that depth for a few seconds. My second dive is an FRC to about 15-20 feet and only about 20 seconds total. My third dive I lay on the bottom and try to get my legs to lay flat on the bottom instead of curled up. I find that simply laying my legs on the bottom straight out behind me has this weird way of relaxing me.
Then I start diving with a purpose!
Side note---What I described above might seem like a lot of time but it's really only about 20 minutes at the house and about 15 minutes on/in the water. Most days I'm in the water for 3-5 hours so 15 minutes isn't much. But even if I'm only going to be out for an hour I still warm up the same way because it allows me to get the most of the time I spend on the water.