This great question comes up very frequently by my clients during my initial conversations with them or at some point after their lawsuit has been filed. 

In general, if the Defendant in your accident case has insurance, it will, by terms of the insurance policy, provide a defense of the lawsuit you file.  This means that after the defendant is served with the suit, the individual will forward the suit papers to their insurer.  The insurer will then hire a law office or attorney to represent the defendant.  The law office the insurance company hires could be its own staff counsel (which are actually employees of the insurance company) or "outside counsel", which bills the carrier, usually on an hourly basis.  

If the defendant's insurance carrier has disclaimed coverage, it may not provide an attorney and the individual must find counsel to represent their interests out of their own pocket.