I am not sure what you mean here (I am only just starting to learn electronics).
Do you mean add a second capacitor between Vin and Ground on the input and Vout and Ground on the output in parallel with the existing capacitors?
I think I am using bog standard electrolytic capacitors. Are ESR capacitors different?
You need to include the capacitors specified in the datasheet. As I would interpret it (they give very little guidance other than the suggested schematic, I would pick a 0.1uF and 10uF ceramic capacitor.
Electrolytics have high ESR (equivalent series resistance - nonideality from resistance in the leads and material of the capacitor that acts like a resistor in series with it), caps with an ESR outside the range the regulator is designed for can cause poor load regulation. Small ceramics are needed for decoupling on the input and filtering the output. Larger bulk electrolytic caps are not harmful (they can improve stability in the face of large load changes) but they do not replace the specified capacitors.
Also, that datasheet is so lousy that I'd have picked a different 1117-series regulator that gave explicit guidance on what types of caps to use.