The way for lawyers to feel about defending clients they believe to be guilty?

ALL defendants are innocent until and unless one of two things happens.

1. The defendant admits his or her guilt by pleading guilty; OR,
2. A jury finds the defendant guilty.

Yes, it is just that simple.

The burden is on the state to prove a defendant is guilty. If the state does a good job amassing evidence of guilt, and if the crime charged is appropriate, then a defendant will likely plead guilty.

It is the job of a criminal defense attorney to make the state prosecutor do a good job of amassing evidence and using that evidence appropriately, without violating the rights of the defendant.

If the prosecutor does not do a good job, if the police did not do a good job, if the charges do not track the facts, all of these people have contributed to the failure of the prosecution. If the defendant did not participate in the creation of circumstances and facts which establish his or her guilt, the defendant is not guilty of that with which he or she was charged. The defense attorney challenges the evidence and the procedures of the prosecution -- and if the evidence and the procedures do not hold up under scrutiny, then the defendant will be adjudicated not guilty or the judge will dismiss the case.

There is a lot for a defense attorney to do: Remember that the state's prosecutors sometimes overcharge defendants with more than the state can prove. This allows the prosecutors to bargain on the charges and offer the defendant a chance to "plead down." So, if a defendant is charged with several crimes, the state can dismiss some for a guilty plea. The state can also make recommendations to the court as to what sentence might be appropriate considering the defendant's culpability, the crime, aggravating factors (tending to make the crime worse) and mitigating factors (tending to make the crime less egregious). Also, a defendant might offer information about other serious crimes of which the defendant has knowledge to obtain a better deal.

“If you can railroad a bad man to prison,” says Cook, “you can railroad a good man. That’s why we should always vigorously fight for the constitutional rights of even those who are most despised in our communities.”

Additionally, It is the responsibility of an attorney to serve as an advocate for the client.

It is not the responsibility of an attorney to factor in, or serve as an advocate for, societal views or interpretations of the guilt or innocence of his/her client.

It is the job of the prosecuting attorney, to prove a case against the client.

So, the prosecuting attorney presents the best available evidence for conviction and the defense attorney presents the best available evidence for acquittal.

Most people don't understand the full value of having a professional advocate on their side in our adversary system of justice until they're in trouble.  As the old saying goes "Lawyers are bad, until you need one".

Attorneys understand their role--it's drilled into them in law school--so at the end of the day they focus primarily on how well they represented their client given the evidence at their disposal. 
    
Any cognitive dissonance associated with representing a guilty client, or helping to get one acquitted is counterbalanced by:

1. Knowing that our justice system was established to make the burden of proof the state's responsibility, and
2. Knowing that our justice system would rather set a guilty person free than convict an innocent one, and
3. Knowing that they have fulfilled their role in that system to the best of their ability.