Having read the other answers, they seem to hit most of the right topics.
- You start with a basic formula to get a good idea of what it should cost, perhaps using previous sets examples. (Not as easy if its your first set, mind you...) This is the cost recommended by design.
- You tweak the card on an individual basis to emphasize or deemphasize particular mechanics and combos. This is usually called 'devign' - it's a stage between design and development. Development may send something back to design, or they may make minor changes in devign.
- You play the set over and over and over again to make the set balanced. This is development.
And in summary that's a great start. But there's something that's very important: Wizard's intentionally makes bad cards. Or do they...
Consider Lightning Bolt. It's a killer spell. 3 damage, instant speed, 1 mana. Awesome. Then consider Volcanic Hammer. Same 3 damage, but sorcery speed and 2 mana. Umm, what happened here? What a bad card. Well, it WOULD be a bad card if that set had Bolt in it, but it didn't. Chances are they had something like Bolt in there, but it was too powerful. Maybe they tried Shock and found that it was still too powerful. So they made it 3 damage again but tacked another mana on it. But then maybe they found it STILL too powerful, so they made it sorcery speed. In 2002, Hammer was seeing tournament play. How could a bad card like that be tournament playable? Because it was balanced, and still a good card. It just wasn't as good as Bolt, so people considered it bad. If they made a card called Super Lightning Bolt, which did 4 damage for 1 at instant speed, everyone would start burning their bolts in a huge fire to make room in the collections for this new one. And then when regular lightning bolt is in a new set, they'll whine about how bad it is compared to super lightning bolt.
But then there are other cards that are just... well... bad. Dragon's Claw is a great example of this. It's really not a good card. You spend two mana and maybe gain four life over the course of the game. Well, those two mana could have gone to a Headlong Rush that obliterates your opponent's board state. But dragon's claw is a catchy card that new players like. If it cost 1 and you got to draw a card, it might see play. (This was why things like the spellbombs saw some play in Scars - they replace themselves, which is honestly one of the biggest costs to things like dragon's claw.)
So as you go making your cards, don't think that each card needs to be great. You're always going to have a top 10%, a middle 60%, and a bottom 30% no matter how good you make your cards. So make sure you design them with that in mind from the beginning.
I would start reading the Making Magic column. Mark Rosewater spends a lot of time helping other people get better at what he does for a living. Once you've gone through a lot of that, he answers questions on his tumbler and he occasionally entertains questions from aspiring game developers. (Note that he cannot review unsolicited material so your questions need to stay high level.) Every article of Making Magic I've read has helped me as a developer.