You have several options:
Professional Appraisers
...are often the best route to go if you've just inherited a collection and need it appraised for legal purposes. They are impartial however they are not specialists in the coin market so you may not get a completely accurate price as far as retail value goes. They also charge a fee for their service.
Coin dealers
...are specialists in the coin market but they have a vested interest in the collection, especially if you're appraising it with the idea of selling it. Many dealers will give an appraisal for free, but if you decide to go to a dealer be sure to go to more than one to get a more accurate idea of what the collection is really worth and who will give you the most money for it.
Professional Grading Services
...grade just one coin at a time, and you usually have to pay a membership fee. This fee is often so high that it is only worth it to subscribe if you know you will be submitting several valuable pieces. A grade is not a price; it is a ranking of the condition of the coin. The advantage of a definitive grade from a professional grading service is that a specific grade leaves a lot less leeway for haggling than an ungraded piece. However the cost of grading often outweighs the value of the coin, so reserve grading for pieces that you know are valuable to start with.
Where to find them:
Appraisers, dealers, and coin shops can be found in the phone book. Two grading services that have websites are ANACS and PCGS.