The "Middle Stages" consists of roughly the 4th-6th blind stages.  By now the field should be down to around 6 or 7 players.  There is variance though, as some sit n goes take longer than others. 

The middle stages are a crucial time of play, as blinds are now putting pressure on players.  Also, it is important to become aggressive at this point, as you want to build a decent stack for the late stages.

One way to build your stack is to make smart bluffs.  By observing players during the early stages you should have a good idea of who is weak and can be bluffed.  Say you have 89c in the big blind, and it is folded to the small blind.  Your observations have told you that this player is weak, and has folded on the flop to bets in the past.  The flop comes 6-10-3 with one club.  If that player checks you need to bet.  Since he has been a passive player, he is very likely to fold.  If he doesn't fold you still have a gutshot draw as well as a backdoor flush draw.

Now let's say that the player calls your bet.  The turn brings a Q (not a club), and he checks again.  By his play you can either put him on a straight draw, or a low pair.  Since he is a passive player, you should bet out again.  A pot size bet should make the player fold.  If he calls this bet then you have to give him credit for a hand, and you should check/fold the river unless you improve.

Another play that you need to make is a continuation bet.  This is unlike the early stages example, where you check/folded AK when the flop came bad.  Let's say you have the same hand, AK.  You put in a 3x the big blind raise, and the big blind calls.  The flop is 642, and the big blind checks.  It is very likely he has a big unpaired hand like KQ.  Because blinds are growing and you need to build a stack, you can no longer play so conservative.  In this situation you should make a pot size bet, and if it is called check/fold the rest of the hand unless you improve. 

One more important concept you need to learn is how to play hands against chip stacks.  Hands should be played differently depending on who you are in the hand with.  You should usually avoid bluffing large stacks and short stacks, as both are more likely to call. 

One tricky play you can use is slow playing certain hands.  If you have AK in the big blind, and the small blind, who is a short stack, raises you, you can try just calling.  Raising here might scare him off if he has a decent amount of chips left, but if you just call he is almost certain to go all in on the flop.

During these stages don't be afraid to get all in preflop.  If you hold JJ in the big blind, and an aggressive player with an average stack raises from the small blind, it is correct to go all in here.  If you just call, the flop could come bad, and you put yourself in a hard position.  Since the other player is aggressive it is likely he is trying to steal blinds and will fold to your reraise. 

The middle stages is the time to start building a stack.  Blinds are still reasonable, so you can outplay people without feeling pressure from blinds.  If you can build an average stack you'll be in great shape for the late stages.