I'm doing all my stuff in Blender. It's completely free. Max, Maya e.t.c. is pretty expensive. You can do the same stuff in Blender. For Blender, you would need to use CryBlend/BCRY (BCRY is basically a newer version of CryBlend). I won't go into detail about all the possible exports, but to get you started, I guess that I'll briefly explain the static geometry (.cgf) export.
First install BCRY (search youtube for "Blender how to install addon"). Now open the CryBlend/BCRY menu inside of Blender. There should be a button which is named like "find rc" or "choose rc" or something like this (and the same for textures).
Klick it and then go to your engine folder (not the game project folder). Go to tools then rc and select rc.exe. This is CryEngine's resource compiler.
Then you basically just model your object, create an UV map and apply some textures to it (watch some youtube tutorials). A good source for textures is http://www.textures.com
You should watch some tutorials about texturing.
If you need collisions (so that you can't walk through your model), you will have to create a proxy object aswell or directly physicallize the model (generally not recommended due to performance issues).
So I assume that you will use a proxy (just a low poly version of your model) for collision.
Now select your object and apply your materials. There is a specific naming convention for materials.
Any material needs to be named line that:
The ExportName is the name of your model (the name that CryEngine will get). 001 is the submaterial number. So your second material would be 002, the third one 003 and so on. You just count up.
MaterialName can be frrely choosen by you. It is the submaterial name in CryEngine.
For physInfo there are multiple options. The three most basic ones are physDefault (the Object will be physicallized. Use it if you don't have a proxy model. But we want the proxy to handle the physics. So physDefault should not be used frequently. I have only used it for cloth simulation). Then there is physNone (material will not be physicallized), which is what we want in our example (the proxy should handle the physics). And there is physProxsNoDraw. This is for proxy models (physicallize it but hide it).
So in our example let's say you want to export an object with the name "AwesomeCube".
The material on this cube would be named like that:
The material on your proxy would be named like this:
There are more phys types, but I won't cover them now.
All right. Now that you're done, select your model and the proxy. Apply all their transformations (you can do that from the CryBlend/BCRY menu), then (with both still selected) hit "Add Export Node" in the CryBlend/BCRY menu. Choose .cgf and give it a name. In pur example AwesomeCube. It needs to be the same name that you choose for your materials.
Now your objects are ready for export. Inside the CryBlend/BCRY menu klick "Export to Game" and tick "Do Materials". Then klick "ok".
You'll now get a .cgf and a .mtl file (and since newer CryEngine versions a .cryasset file). Copy these into your project's "Assets" folder.
Now inside the CryEngine Editor you should find yor object as a brush with the name "AwesomeCube".
Place it into the level. For setting up the materials just open the material editor. Klick on the picker and select your "AwesomeCube". This will directly open the material for you. You will have two submaterials (surprise).
Select the submaterial "MyProxyMaterialName" and choose a "NoDraw" shader and surface type.
Then choose the "MyMaterialName" submaterial and assign a shader and surface type.
Assign your textures to it and choose the diffuse/spec color and glossiness e.t.c.
That's basically how you import objects. The steps for max and maya are similar but it is differently done. But you have for example the same phyaics options e.t.c. in max and maya. So the basic export process is similar.
Now you should first watch some youtube tutorials about blender (specially: modeling, UV maps, texturing), CryEngine's "Material Editor" and other basic stuff.
Some short fun facts:
1. You can create all your textures with GIMP. Just export them as .tif (for _ddna make sure to tick "export color values from transparent pixels" on export). Then create a shortcut to the rc.exe on your destop. Right click it, go to "properties" and after the target path add /userdialoge=1(I guess it was this line. I'm not 100% sure here). Then drag and drop your .tif onto the shortcut to the rc.exe. It should now open a window to convert your tif.
2. An export node in CryBlend/BCRY is just a normal Blender Groupe. So you could even manually assign objects to it or manually delete them from the groupe and other stuff.
I hope that this was useful. Feel free to ask if you have any questions.
p.s.: I know that this is a pretty long text. But I thought that I should go into detail here, so that you can get a step by step guide.