Termites are flying inside my house. What should I do?

Don't Panic

Firstly, put down that can of fly spray.  It really won't help.  Grab a few termites and put them in a plastic bag or a glass in the freezer.  You may want these later.  Gather up the rest (broom or vacuum).  Maybe feed them to your chickens or fish (if you didn't spray).

Now for the important bits. 

Were the termites coming in from outside (this often happens if you leave a window open or have an outside light left on)?  Termites outside are often just a local hazard.  Walk around to see if you can see them spilling out of any trees, garden wood etc..  Chances are it is just a few stragglers from a normal local flight.  Order a timber pest inspection if you haven't had one for a year (or if the alates were emerging from important timbers like pergolas, fences or your house).

Were the termites coming from inside the house?  Sometimes they'll emerge right out of a wall, through the plaster, often near the top of a window or from a door frame or other feature.  Look for little holes, often lined with brown or red mud and with termites dropping out or termite heads sticking out.  If you have any of these signs, then you have serious problems.  Termites flying from within a house mean that there is a significant termite presence already having fun at your expense.  Take some photos.  Clean up the mess.  Save your sample termites from the kids (or spouse) so that you can get them identified.  Get a competent timber pest inspection.  The termites may fly several times over the space of a few weeks.

Don't be rushed into any control measures.  Consider your situation closely and act accordingly.