This tutorial has been adapted from the community generated Animation Wiki.
First thing you'll want to do is go into System → Preferences and choose the FBX I/O option on the left hand side of the preferences window. There are no options at export time so you need to do this before exporting your animated model. Users find these settings are working well when exporting in FBX 2013 format:
Make sure you choose FBX 2013 format from the drop-down list when you export your animated model.
Sample animation will bake keyframes onto your bones at the interval you specify. This will increase your file size. You should try exporting with this disabled first, and if you notice "swimminess" or inaccuracy in your animation then turn this on and try different FPS settings. 1x FPS means add a keyframe to every bone on every frame, 2x means every other frame, 3x = every third frame, etc.
You should use ACS (Automatic Character Setup) in Modo to rig characters unless you can create your own rigs from scratch. Please refer to the ACS documentation for help setting up your character.
You should Bake the rig before exporting. This will remove all fancy rig controls and other unsupported elements and leave you with a simple keyframe animated skeleton. Make sure to save your file first, then undo the bake or reload your file after you export, otherwise you will be stuck with this skeleton and no longer have your easy to animate rig.
Once you bake the rig your model will be contained within the hierarchy, as the Jack_3 model appears below:
Grab this item and drag it out of the hierarchy to be a top level item (you can drag it up onto the scene name, in this case Jack.lxo):
Important: If you don't do this your model will not show up at all in Sketchfab! When exporting, make sure you have only that main model selected. The entire hierarchy and any child objects (like eyeballs, teeth, etc.) will automatically export into your FBX.