How does one evaluate the "strength" of a hand in Magic the Gathering?
A Good Hand is a Good Plan

Magic plays rather differently from a traditional card game:


Most cards in Magic require other cards as resources (e.g. land to generate mana). They can only be played once you've sufficiently developed your board. An effective deck has a mixture of early-, mid-, and late-game cards; what exactly that means varies greatly depending on your strategy.
Many cards are situationally useful — they're good because of synergy with other cards, or because they're reactive cards that answer an opponent's plays.
You get to tailor the deck to a particular strategy (outside of a few very special game modes like Momir Basic and Rainbow Stairwell).


So, most of the individual evaluative tricks don't work the same way at all. But that's fine.

Because, as you probably know, all of the evaluation tricks from bridge are cognitive shortcuts for figuring out the fundamental question: "How will this hand play out?" That's what you need to figure out in Magic as well.

Look at your hand and imagine what you're going to do in the next few turns. Imagine what your opponent is going to do, too, based on whatever information you have about them.

"I'm going to run my opponents out of trumps and then all these low cards will be tricks."
"I'm going to play some cheap creatures and use burn spells to clear the way while they apply repeated pressure."
"I'm going to use counterspells to survive long enough to cast my Wrath of God, then stick my planeswalker to control the board." 

A good hand is, typically, one that presents some kind of coherent "story" or "gameplan" — ideally one that's powerful, fast, and resilient to disruption.

As a starting point:


What are you going to be doing on turn 1, turn 2, turn 3, et cetera?
Do you have enough lands to develop your board?
Do you have cards you can play early to help you stall or put pressure on your opponent? (Which do you actually need to do: stall or apply pressure? a.k.a. "Who's the beatdown?")
What's your opponent likely to do to disrupt you? What can you do to do to disrupt them?
What's missing? What cards do you need to draw to shore up your weaknesses or make your strongest play? (A bit of poker experience may help here. It also helps to understand "playing to your outs.")


Note that, beyond basics like "Make sure you will be able to actually cast something," what actually constitutes a good or bad hand is highly situational. Familiarity with your deck, with the metagame, and with general archetypes and strategies will all help immensely here.