Welcome to the site.
There are several options for selling online. Some are good for quick flipping sales while others will take awhile. Some sites are good for selling quickly while others take some time to sell. Also remember no matter where you sell them don't expect to get their full value. To be a bit optimistic you could get somewhere between 25% - 50% If you are lucky you could maybe get about 75% of their value. Even getting about 15% -20% would be be possible.
First off find out what you have. To be brutally honest, If most of it is from the years 1985-1995 (give or take a couple of years) then it is practically worthless due to super overproduction, often called "Junk Wax Years". The actual dates people debate about but Readers Digest version: from about 1984 to about 10 maybe 15 years later there were several dozen card companies each making dozens of card sets per year, overproducing cards by 10s of thousands maybe even by the millions, plus "collectors" back then were mostly "investors" thinking that they could buy out a couple dozen rookie cards of the latest stars and then make money 20 or 30 years later. The end result most cards from that literally go for a dime a dozen, or more often several dozen. Best to donate them to some children's organization, or recycle. Don't throw any away.
The most popular always seems like Ebay. It is the best place to find out the current worth of things by looking at completed sales, not what things are listing for but what they actually sold for recently. (even if you don't sell on Ebay itself it is a good price guide) However it is the most competitive. Unfortunately there are also a few scammers around (both sellers and buyers) who are looking for quick bucks. The scamming seems to be random, some members never have any problems with them while other people seem to be infested with them. Selling on Ebay means you are responsible for everything, researching what you have and seeing what is a "fair" price, you are responsible for everything, the listing, the scanning (I think Ebay nowadays insists on having good quality photos/scans of every listing), setting the price, packing, shipping, everything. There are several sellers fees that turn some people off from selling on Ebay, but it is one of the most popular and better seen places.
There is also Sportlots, which again is a site where you do all the work, and shipping. I think there is also a way to send stuff to them to ship out, they have some kind of deal for overseas sales where the sellers have to ship to a central location that gathers the sales and bundles sales from several sellers together to help people in other countries save on shipping costs. I have not sold there so I don't know all the details or cons of selling there. One negative for selling is you have to list by card, unless you set up your auctions for card lots.
There is also (I think already mentioned) COMC (Check Out My Cards or Check Out My Collectibles) you are responsible for setting prices, but you send your stock to their warehouse and they handle the shipping end of the sales. This is one that might take a whle for the cards to actually sell, but if you don't want the cards taking up your space it is a good way to go.
Another option is to try you luck at a local card shop to see if they will buy the entire collection. You won't get top dollar but you might get rid of all the cards. If you are in the US or Canada this site could help find one near you: http://cardshopfinder.com/
Also if your area has flea markets (or a similar type swap meet) you could look into how to set up a selling table and hope you can unload stuff.
As a collector the one thing I absolutely hate in this day and age is when people have given up all hope and just "trash" the cards. I would rather see them get recycled or given to some place that will find a place for them rather than going to a landfill somewhere. Ultimately I would like them to go to an actuall collector that will appreaciate them.
I collect: Baseball, Football, Hockey, Mostly Vintage pre1980, My Homie teams - Washington/Baltimore Teams Senators (Twins, Rangers), Expos/Nationals, Redskins, Capitals, Bullets/Wizards - HOFers - Non-sport (mostly TV shows and movies).
My Trade List is very much a work in progress
CaptKirk42s Trading Card Blog Curly W Cards Strive For '65 YouTube klandersen42