Of all the techniques used to conceal nail or screw holes, blind nailing is my favorite. Blind nailing can refer to one of a few different practices. In today's modern usage of the term, it perhaps refers mostly to the securing of nails at a 45 degree angle into the top, inside corner of the tongue on a tongue and groove board.
By installing the next board the nail will be covered and thus hidden from view by the incoming groove. In this way the installation is continued until completion. The final boards are nailed straight down but are done so in a location that will be covered by trimming or similar.
But aside from the above kind of blind nailing, there is another older form of it that serves another slightly different purpose. This is the practice of taking up a chunk or chip of wood with a chisel or similar, under which you sink your nail or screw. You then glue your chip back on over the nail and sand it down smooth after it dries.
This may seem primitive or old-school but it's surprisingly efficient when all else fails. Just make sure your chisel is sharp and you do it carefully, as the end result depends on how clean your initial cut is. The trick is to make the cut without "cracking" it off completely – although it's not the end of the world if this happens.
If you do accidentally remove the piece completely, you'll simply need to glue it on in the same way. Just note that any "splintering" across the grain is very difficult to reconnect well. So to ensure the best results, you should choose the most inconspicuous places as possible so that if there is a slight imperfection, it won't be so visible.
For those who aren't so good with chisels, there are tools available for this exact purpose. These tools are called blind nailers, as is, and look like a planer but with a chisel blade. This tool will make this job considerably easier so I recommend it for beginners – or for those who simply can't afford to make mistakes.