Be aware of export scope e.g. meshes, cameras, lights, animation rigs, etc.
Applications often let you export selected objects or a whole scene
Make sure you are exporting only the objects you want to use from your scene by either exporting selected, or removing unwanted data from your scene.
Good working practice often means keeping a working file with all lights, guides, control rigs etc. but only export the data you need with export selected, an export preset or even a custom scene exporter.
What do you need to include?
Prepare your assets:
Meshes - Remove construction history, Nurbs, Nurms, Subdiv surfaces must be converted to polygons - e.g. triangulate or quadrangulate
Animation - Select the correct rig, check frame rate, animation length etc.
Blend Shapes / Morphing - Make sure your Blendshapes (Maya) or Morph targets (Max) are assigned / set up the export mesh appropriately
Textures - Make sure your textures are sourced already from your Unity project or copied into a folder called \textures in your project
Smoothing - Check if you want smoothing groups and/or smooth mesh
How do I include those elements?
Check the FBX export settings
Be aware of your settings in the export dialogue so that you know what to expect and can match up the FBX settings In Unity - see figs 1, 2 & 3 below
Check Animation / Deformations / Skins / Morphs as appropriate
Nodes, markers and their transforms can be exported
Cameras and Lights are not currently imported in to Unity