The Steam trading cards are irrelevant to most people. No, you don't all get the same cards when you play. They're random. That's what makes people need to *trade* them.
Once you have a full set, you can craft a badge, which will affect your Steam level, which will affect emoticon sets in chat, backgrounds, maximum friends on friends list, etc. Most people really don't care about the trading cards tho.
"How do I get rid of a Trojan Horse?" -Sailor_Kakashi "Leave it outside the gates of Troy overnight." -Davel23
The questions to ask yourself are: 1) Do you like leveling up something that doesn't really change that much with each level? 2) Do you need more than 250 or 300 friend slots? 3) Are you a sucker for badges? 4) do you often wish you could have a background of your favorite game for your steam profile? 5) Have you ever thought to yourself: "Boy I wish I could just type :alyx: in chat and have her face appear"? 6) are you willing to spend money or time trading cards between other like-minded people?
If so, then fear not! Trading cards are here to save the day!
For trading card enabled games you just play like normal and you'll get a certain amount of cards for FREE! (half the amount necessary to earn a badge)
So to get the rest, you'll have to bug your friends and annoy strangers with requests for cards that they have but YOU need (they don't need them, you're far more deserving!). Don't have any friends to bug or you're not sure how to approach strangers without getting blocked? Buy them on the steam market! For just pennies* you can buy cards to fill up the rest of your collection and earn that coveted** badge!
* actual price my vary by quite a bit ** not everyone covets them, but if you do, well... cool I guess.
Alternately you can sell them on the steam market for game funds towards your next purchase. Think of it as an "idiot tax" and you're the tax man!
Offer void where prohibited, operators standing by, some assembly required, batteries not included. Your mileage may vary.