The optimum distance between the top of the twelfth fret and the the strings on a soprano or concert ukulele is about 2.5-3mm. have found that ukes supplied by shops generally have a much higher action, so it is usually necessary to have any new instrument set up.
To lower the action, the saddle needs to be removed from the bridge so you can remove material from the underside. I found that wet & dry paper taped to a flat surface is good for this.
After adjusting the height at the bridge, the string slots in the nut can be adjusted so the open string sits as low as possible in the nut without touching the first fret. People have reported success in using a welding tip-cleaner as a file for this, however I managed with some wet & dry paper folded over a thin knife blade.