I'm not a pro, but using a sharp lens, making sure the lens is clean, making sure there is no unwanted blur, setting the correct depth of field, getting good contrast in the shot, good post processing technique and an appropriate final size all play a part.
You really won't see a difference in terms of pure sharpness between aps-c and full frame with all other things being equal, but there are some areas where using a full frame camera will produce a better result than an aps-c. Full frame cameras have better low light performance, for example. This could then have an impact on sharpness, because you typically need less noise reduction in post, or you can get cleaner shots at higher ISOs allowing you to use a faster shutter speed.
So sharpness is not one thing, but has a multitude of factors that can have a role.