To get accurate appraisal you would need to find out as much as possible about the model, manufacturer, condition and production information. Here is the list of basic info you will need:

• Type of firearm (handgun, pistol, revolver, shotgun, rifle…). Please, include if it’s muzzleloader or does it take shells; if it’s a handgun or revolver (with a rotating cylinder holding the rounds) or autopistol (with removable magazine); If it’s long gun, is it shotgun or rifle.
• Type of action - What type of action does it have – single shot, break-open, double barrel, bolt action, pump action, lever action, revolver, semi-auto, other? Double or single action? Exposed hammer or hammerless? If revolver, solid frame, tip-up, top-break, or swingout cylinder?
• Caliber - sometimes this is marked. Otherwise, give an approx. measurement of bore diameter
• Measurements - barrel length, overall length.
• Markings - if you know the make & model - or just list all markings on the gun.

Condition – After you know what it is, the biggest factor in value is the condition of the gun.
Differences in condition can easily halve or double the value of a gun.
This is a somewhat technical evaluation, and if you’re not familiar with guns, you probably won’t be able to do it, and should ask help.
There are two systems commonly used: NRA Condition Standards and Percentage System.

The NRA Condition Standards:

• modern guns as New, Excellent, Very Good, Good or Fair
  
• antique guns as Excellent, Fine, Very Good, Good, Fair, and Poor. 
  
Each condition rating has a specific definition.

The Percentage System rates the percent of original finish remaining on the gun - 100% to 0%.

Please note that refinishing a collectible gun or modifying it or customizing it or over-cleaning it nearly always lowers the value.
NEVER take it upon yourself to clean up an old gun unless you know what you’re doing. I’ve seen folks buff a $2,000 gun into a $200 junker!