You still have to export your textures as png/tga/jpg/… files - then import all textures - right click onto them - create new material - assign the material to your mesh 
But there are also ways which will allow you to export your textures with the mesh, but then you still have to modify the material a little bit (so it will just import the mesh + the textures + it create a basic material) https://forums.unrealengine/showthread.php?51311-Import-FBX-properly-with-textures!