I had the same situation. Received a huge collection from my grandfather in 1994. Get a 2014 Red Book of coin values ($13.45 on Amazon). Good reference for pricing and figuring out what things are. Search completed listings on eBay. Check out PCGS for full retail, graded coin values.
To accurately value each coin, you need to know the grade. This is easy if the coin has been officially graded by a service (it will be enclosed in a tamper-proof plastic case). If not, it's up to you or an appraiser to determine this. The coin grade can affect the value dramatically. There are general grading guides (Red Book), but accurate grading is accomplished by someone that's been looking at coins for a long time. Usually, inherited coin collections are pretty extensive. Mine was, so an extensive appraisal was cost prohibitive.
Over the last 13 years, I've been selling off this collection on eBay. You can sell individual coins and rolls for retail or very close to it. The beauty of eBay is that if you are a reputable seller and take honest, non-enhanced high res pictures of the coins, the buyer determines the grade. While I have a decent grading sense now, I never list the grade of the coin in the description. Let the coin speak for itself.
Personally, I would stay away from coin dealers. In my experience, they really try to peel your collection. Obviously, they need to buy to make money, but there are a lot of unsavory dealers around.
If you want to maximize the value, use eBay. You have to take really high res detail pics. If you have the time (and that's a big if) this is the way to do it.