Optical micro- and nanofibers have recently gained popularity as tools in quantum engineering using laser-cooled, neutral atoms. In particular, atoms can be trapped around such optical fibers, and photons coupled into the fibers from the surrounding atoms could be used to transfer quantum state information within the system. It has also been demonstrated that such fibers can be used to manipulate and trap silica and polystyrene particles in the 1-3 mu m range. We recently proposed using a focused ion beam nanostructured tapered optical fiber for improved atom trapping geometries'. Here, we present details on the design and fabrication of these nanostructured optical fibers and their integration into particle trapping platforms for the demonstration of submicron particle trapping. The optical fibers are tapered to approximately 1-2 mu m waist diameters, using a custom-built, heat-and-pull fiber rig, prior to processing using a focused ion beam. Slots of about 300 nm in width and 10-20 mu m in length are milled right though the waist regions of the tapered optical fibers. Details on the fabrication steps necessary to ensure high optical transmission though the fiber post processing are included. Fiber transmissions of over 80% over a broad range of wavelengths, in the 700-1100 nm range, are attainable. We also present simulation results on the impact of varying the slot parameters on the trap depths achievable and milling multiple traps within a single tapered fiber. This work demonstrates even further the functionality of optical micro- and nanofibers as trapping devices across a range of regimes.