Determining when to mulligan is a very important skill in magic. But how can I hone my abilities in that skill? Obviously if I had no/all land I'd probably want to mulligan as the opportunity to actually cast some of my spells are worth the 1 card penalty. But what about when I only have 1 land or 1 spell? Are there any good rules of thumb to help me make this decision? How can knowing my deck make these choices easier? What other elements of my hand should I look at when making this decision?
Unfortunately, knowing your deck inside out and comparing your draw against it are the only universal rules that can apply, so it's a highly individual decision that depends on those two factors. If you already have a good idea of the opponent's deck, that also helps, of course. Essentially, experience is where it's at.
You can ask yourself a few questions.
Note that if you often get into a situation where you must consider mulligan (assuming careful shuffling before each game), then there might be an issue with your deck. Adjust the number of mana sources and/or the mana curve of your spells.
On shuffling: obviously, good shuffling is essential to let your deck design have effect on reducing the number of necessary mulligans. During the course of a game, card types tend to clump together as you arrange them: Lands, creatures, and artifacts you play get close to each other, and after the game, they will probably stick together. You have to separate them thoroughly, for example by multiple pile shuffles:
Especially in tournaments, take your time for shuffling, though of course not so much that it could warrant a warning.
Edit: Thanks to thesunneversets for the reminder about first to draw or first to play, +1 for that. Another thing I would like to add on that matter:
If you play it very straight, then the player who is first to play is also the first to announce whether to keep or whether to take a mulligan. Only after the first player has finished all his mulligans and announced to keep his hand, only then does the second player have to start announcing mulligan or not. Therefore, if you are first to draw, that can be a very important factor in your decision whether to mulligan or not. If your opponent has to mulligan, then you can either risk playing a sub-optimal hand because of your card advantage, or you can mulligan as often as he does for a chance of a better quality hand.
On the other hand, if you are first to play and consider mulligan, then you can in a bit of trouble, because everything you say or how long it takes you to say it can be a signal to the opponent. If you take a long time to decide whether to mulligan or not, then this can be understood as a signal that you are not happy with your hand, even if you decide to keep, and that can influence your opponent's choice of mulligan or not.
That way, magic can become truly a mind game like Poker beyond the logic of rules and numbers. This applies to the whole game, not just the mulligan phase.
In the old days, mulliganing was easy. No lands? All lands? Draw a new hand.
And then along came the Paris Mulligan - now a mulligan is always an option, not just a get-out-clause for an absolutely unplayable hand. And while you will certainly still always mulligan an all-lander or a no-lander (unless your deck is EXTREMELY unusual), there are many more borderline cases where you will have to make some tricky choices.
Hackworth has already provided a useful list of things you should be thinking about while deciding whether to take a mulligan, and I've upvoted that, but here's a couple of things that I feel compelled to add:
Beginning players, and I remember well that I used to be like this, have the mentality of "this will be a great hand... if the first card I draw is a land. What the hell, I'll keep it!" Thinking like that probably gives you a 60% chance of losing even before you play a single card, not good odds! Being a card down is bad news, but it's much less bad than running the risk of not being able to play your deck at all. Think through all the probabilities, and then, if necessary, mulligan away. I think it's fair to say that having a good sense when to mulligan is one of THE major factors that distinguishes the pro players in the game...