Select Export to engine from the File menu.
This will write the level data into the level.pak file that is read by the engine in pure game mode.
Select Generate Triangulation from the AI menu.
This will write the AI triangulation data into the level.pak file, which can be read by the game in pure game mode. Without this information they AI can most likely not navigate through the level.
Click Generate surface texture in the File menu.
This will write the painted ground textures to the terraintexture.pak.
For final quality use 16386x16386, high quality, calculate terrain sky accessibility. For testing the default 4096x4096 is fine.
Start Crysis.exe.
Press the button left next to the number 1 button of your keyboard to bring up the console:
Type in con_restricted 0 to unlock the console.
Type in map "yourlevelname" (without the "").
Pressing ENTER will load the level.