There is an art and a science. The science is what others have said -- keep tracking your reservation, keep switching your seat to where nobody is sitting next to you. If possible, if you can get an exit seat at the last minute (say, all the elites have upgraded out of that seat) then you can reduce your odds of someone like a mother with child taking the seat, since 15 and under, and the very obviously inform person, can't be seated in the exit row. However, if there are a lot of standbys, then those seats are going to be filled anyway, and all your hard work goes for naught.

As for the art to it, well, in 2009, I was twice seated next to the ONLY empty seat on an otherwise completely full flight. On AMS-ATL, it was pure quick thinking, I saw that the only empty seat in the cabin was an aisle seat and I advised my lady in the middle seat to QUICKLY ask the FA if she could have the seat, the minute the doors were closed. The FA said yes, so scoooorrreee! She gets a better seat, I get elbow room. On the other flight, MIA-VVI, I can only credit lucky chance or maybe crystal power. The seat next to me was taped up as broken. Just in case the magic crystals didn't want to do all the work, the second time I booked that flight, I went ahead and sprang for business...

Also, booking a VERY empty flight can really backfire. My original AMS-ATL was the day before and very empty, with lots of room to spread out. They cancelled it and combined the flights. Yes, with plenty of warning ahead of time so I could have backed out of the trip if I wanted to...but still...not that many planes are going out these days with oodles of empty seats.