If it's been awhile since it was tuned (>30K miles), I'd replace the spark plugs, air filter, fuel filter and PCV valve. If it has a distributor, also replace the cap and rotor. You can probably do all that yourself with a minimum of tools, a couple of your favorite malted beverages, and a rag or two..and a savings of at least 1/2 of what the local shop will charge you. A pressure clean of the injectors is an excellent idea given the miles on it.

If the car still has problems, then it's going to require a deeper level of diagnostics. Have fuel pump checked first, if that's ok then have them hook it up to Mr. Computer to find out what it thinks it's doing.

Some of the sensors that could affect cold start are: Mass Airflow, Oxygen, Manifold Air Pressure, Throttle position, engine temperature, ambient temperature, and vehicle speed (not all cars have all these sensors...). Also, some cars have a device called an IAC, or Idle Air Control motor. Those are all the inputs to the computer which it uses to determine fuel/air mixture, fuel volume, and spark timing. The proper equipment can query the car's computer as to what values those sensors are reporting and further enable the mechanic to understand what's wrong. Note that these parts can run into some serious money.