There isn't a simple one click solution to this problem. You must have at least one, and preferably several images of cherry blossom petals with an alpha channel (transparency) so that only the petal is visible. Then you need to move them around in 3D space.
The fastest way to do this is to use a particle system like Trapcode's Particular and a short sequence of individual images of a cherry blossom petal. The sequence of images is used as a custom particle and the physics are adjusted to achieve the effect you want.
You can also accomplish the same thing manually by taking several individual images of a petal and animating them in 3D space. I hope this points you in the right direction.
For the non-Particular solution Rich suggested you could use expressions to get some nice pseudo-random motion. With a bit of fiddling you can also use other particles systems like CC Particle World, CC Bubbles or even Card Dance, but in either case you need a few nicely cut out petal images first...
vague statements like "animating them in 3d space." isn't really saying anything productive.
i got to tell ya, i really hate the way this program works.
the interface is terrible.
too many things have to be done manually.
i'm sure it can't be THAT hard to make some REAL petals look like REAL petals floating on the wind.
the more these programs change, the more they stay the same.
Then quit while you are ahead! I'm sure there are more people around who have successfully been doing this stuff for 20 years and that will bother you with even more vague comments and suggestions on working with that awful program...
If you want physics (real) motion, then use a particle generator plug-in like Particular. EZ as pie. A little more complex is Particle Playground, which comes with AE, but that will take some effort.
If you want to do it by hand then you've got to, by hand, do all the physics calculations yourself manually, which is very hard.
If you want to use built in psudo 3D effects based on existing templates then look for a pre-built AE project (there are a bunch of suppliers, check the WEVA site for links to this kind of stuff) or use Motion. It makes no difference what program you use from the highest end 3d to the lowest end image editing, if you want to create a realistic simulation of flower petals floating through the air on wind currents by hand it's going to take a ton of work. The only other option is to spend money on a plug-in that calculates the physics for you. The more you spend for a program, the more likely a good plug-in will be included. One of the best out there is Real Flow (fluid simulation). You can buy it here. It's only about three grand....
Nothing's free, except advice. What you do with it is up to you.