The importance of keeping a good connection to your fly (or flies) is critical when nymphing.  Here I describe some quick do's and dont's for tandem rig nymphing.

In the above example a strike must take up the slack before it will even begin to effect the indicator.  By the time that happens, chances are the opportunity to set the hook will have passed.

This shows a good connection from the strike indicator to the dropper nymph.  A good connection is one that doesn't have excess slack anywhere in the rig.

If you like to nymph without an indicator (my personal favorite), then the connection includes everything from the rod-tip to the dropper.  Unlike dry fly fishing, you will not have the luxury of leaving a lot of slack in the line to be able to extend your drift.  The drifts will be shorter, so use weight if needed to help get into the feeding lanes quickly.

By keeping the slack off the water, you will be better able to feel a strike.  It's also important to keep a close eye on the angle your line enters the water at.  If that angle changes quickly, it could be a strike.  Give it a strip.  When nymphing free-hand it's better to err on the side of too quick to set the hook than miss opportunities.  If you are new to nymphing, I suggest an indicator of some sort until you get the feel.  Good luck!