Your best bet is to try to identify any specifically valuable individual cards, and then sell the rest in bulk.
For a first pass at identifying the valuable cards, what color is the outermost border (i.e., right up against the edge) on the face side of the cards? Cards have a black border on their first printing, but a white border on later printings, so the black border ones are in general worth more (there are also some with a gray border, but you probably don’t have any of those).
Next, of the black-bordered cards (if any), you want to look for the expansion symbol: On the line between the card’s picture and the text of the card, on the right, there may or may not be a little monochrome icon. If a card has a black border but no expansions symbol, then it’s from the Alpha or Beta run. Even commons and low-usefulness cards from that run can have some value, just because Alpha and Beta are in general pretty rare. If the expansion symbol is a scimitar, an anvil, the top of a classical column, or a crescent moon, then it’s from one of the earliest expansion sets (Arabian Nights, Antiquities, Legends, or The Dark), and likewise has potential for value.
In later sets, the expansion symbol is color-coded to indicate the card’s rarity. Commons are black, uncommons are silver, and rares are gold. They later added a category of mythic rare, which is even rarer and is sort of orangish flame-colored, but you probably don’t have any of those, given the timeframe you mentioned.
In any event, a large chunk of your cards are probably basic lands. These have the name “Plains”, “Island”, “Swamp”, “Mountain”, or “Forest” (or possibly, snow-covered variants of these). These are dirt-common, and go for about a penny a piece (possibly up to a dime a piece, if they’re really old or have really pretty artwork, but don’t count on it).
If you have any cards of type “land” (between the artwork and the text, on the left end) that aren’t basic lands, those have a chance to be worth something. Likewise, if you have any cards that have the word “Legend” or “Legendary” anywhere on the type line, those also have a chance to be worth something. This is true even for white-bordered cards.
For reference, here’s a sample of a card.
The outermost border of this card is black, meaning it’s the first printing of this card. The red border inside that means that this is a red card, but you don’t need to worry about that.
The name of this card is “Ali Baba”, on the top of the card.
The thing that looks like a fireball in the upper-right corner is the cost to cast this card, and means that it costs a single red mana.
The picture is just for decoration, and has little impact on the value (though as mentioned, sometimes prettier art is worth more, and it can also help identify which printing a card was).
The card type (as printed on the card) is “Summon Ali Baba”. Modern cards of this type are listed as type “Creature”, not “Summon”, and the creature types have also been updated, so this card is now considered to be type “Creature-- Human Rogue”, but you don’t need to worry about that.
The expansion symbol in this case is a scimitar, indicating that this card is from Arabian Nights.
This card has a special ability, which is indicated in the text box, in this case “(fireball symbol): Tap a wall”. It also has flavor text, in italics, but like the picture, that’s just for decoration. Any card that doesn’t have any special ability (i.e., just italicized flavor text) is probably going to be worthless.
Since this card is a creature, it has a power and toughness in the lower-right, in this case 1/1. Roughly speaking larger numbers for power and toughness will be worth more, but that’s not reliable. Basically only take note if those numbers are, say, 7 or higher. Noncreatures will lack these numbers.
Once you’ve identified which cards (if any) look like they might have value, look up those cards individually online, or take them to a comic book shop, to find out specifics.
Oh, and if you should happen to find any cards named “Black Lotus”, “Mox Pearl”, “Mox Sapphire”, “Mox Jet”, “Mox Ruby”, “Mox Emerald”, “Time Walk”, “Ancestral Recall”, or “Time Spiral”, forget about everything else, put on white gloves, put that card by itself in a protected envelope, and start looking for buyers. But you’re probably not that lucky.