Clocking Android Netrunner
To be honest, I wouldn't worry so much about slow play when learning, and I would not recommend complicating it further with a clock.  Here are my thoughts:

1) This game requires lots of mental arithmetic, especially when playing as the runner.  How much might that run cost?  Do I have the breaker suite required to make success likely?  What is the worst case scenario?  When you are learning, you can easily fall into analysis paralysis, which will slow the game down.

2) Some more information: Are you playing core only?  Which factions are you playing?  You should know that if you are playing the "FFG Recommended" matchup, Shaper vs. Jinteki, Jinteki is a notoriously slow corp to play/win with, especially against a cautious runner.

3) About tournaments, yes - two hours per game is way too slow.  In a tournament setting, you are typically allotted 65 minutes for two games (playing as both the runner and the corp).  However, because of this, I want to emphasize: decks that play fast are more common in a tournament setting than those that play slower.  For example, one of the most popular builds right now, the "Astrobiotics" deck (an NBN deck that relies on Biotic Labours to score agendas out of hand) is very light on defence and basically crumbles if it doesn't win within the first ten or so turns.  So, there are definitely decks that are really fun to play in casual play, but aren't really brought to tournaments.

4) From the above, know your decks!  If you know exactly what you have in the deck, you will know its strengths and weaknesses, and as you play more, you will start playing it much faster.  

My recommendation?  Play more.  And against other people.  I'm sure there are some playgroups in Seattle you and your friend can show up to.  Learn the cardpool.   Having to read each card as it is played will drastically increase playtime.

BUT, if you are set on using a clock, I would just use it to time how long my decisions took in a given match.  If it is above ~35 minutes, consider what could have been played differently.