How can I find my performance rating? I’ve noticed that in tournaments grandmasters are given a performance rating for how they played in that tournament. Can this be applied to individual games and how can I see mine when I play a game?
Under FIDE rules, the performance rating is calculated by taking the average of your opponent's ratings, and then adding a factor from a table based on performance.  Let's say you played 5 games, against people rated 1380, 1390, 1400, 1430, and 1900, and had 3 wins and 2 losses.  You scored 60%, or 0.6.  According to the table in section 1.49 of this document, in this case your performance rating would be adjusted upward by 72 points.  The average of your opponent's ratings was 1500, so your performance rating would be calculated as 1572.  

The downside to this method is that the ratings averaging can be skewed by one opponent with a very high or low rating.  If you changed the 1900 opponent in the above example to a 2900 opponent and decreased the wins to 2, the performance rating would increase to 1628, even though you performed worse.  If you instead changed the 1900 opponent to a 1000 opponent and increased the wins to 4, the performance rating would go down to 1560, even though you performed better.

The USCF ratings estimator calculates performance rating by calculating how a player at a particular rating would be expected to do against the given opponents, and comparing it to the actual result.  In the example above, a player rated 1563 would be expected to score 3 based on those opponents, so that's the performance rating.  

The downside to this method is that there's not just a simple formula you can figure out in a few seconds.  The upside is that it's less prone to being skewed by one very high or low rated opponent.