When you prepare a spell (or, in case of spontaneous casters, when you cast the spell) you can choose to prepare them with one or more metamagic feats. The slot they take increase, but their level DOES NOT, for all purposes (such as spell DC, stat required to cast, whether a light spell beats a darkness spell and so on).
For spontaneous casters the feat can be applied to any valid spell at any time, but as compensation, casting a metamagicked spell spontaneously takes a full-round action (note that it's a full-round action, not a one round cast such as Summon Monster).
There is no upper limit apart from spell slots to the number of metamagics you can apply; you can make an extended, enlarged, silent, still, empowered acid arrow as an 8th level spell. It would suck though.
Most metamagic feats on most spells make for worse spells than what you could have gotten otherwise. An empowered acid arrow is in most cases a worse spell than a random 4th level blasting spell. Metamagic feats are mostly useful for certain combos, as well as broadening the repertoire of a spontaneous caster (a sorcerer that has good blasts of 1st, 3rd and 5th spell level that takes Intensify Spell will now also have decent blasts of 2, 4 and 6).
The level adjustment can be decreased, though AFAIK only through usage of two certain traits. Each allow you to choose a specific spell and when you apply a metamagic feat to that spell, you may reduce the adjustment by one. I'm not sure on the name though. Also, the spell perfection feat allows you to apply one metamagic feat for free to a spell.
The metamagic feats I think are good feat choices are:
Extend Spell - Has a lot of different usage both for buffs, debuffs, summons and only costs a single level.
Persistant - Borderline too good in my opinion, as a Persistant spell is often MUCH harder to resist than any other spell of that slot level. If you like any kind of debuffs, GET THIS ASAP.
Empower/Maximize - Only for certain combos, stacking up effects to get ridonkulous single effect damage.
Intensify - Increases the max effect of blasts. Just costs a single level and has wide usage as you don't need to get blasts of your highest caster level. If I was only a part-time blaster, I'd rather get this than empower.
Still Spell - For when you're grappled or for any other reason can't move freely. Also allows you to cast in armor.
Also, be sure to check out Metamagic Rods. Especially Silent Spell is wonderful to have as a rod for when you get silenced. A rod of Enlarge can be very useful too - shooting fireballs several miles away is nice. However, it requires house ruling on perception or some other way to see the target.
It's some odd one from some splatbook. Inner sea magic perhaps, I don't know, sorry.
The other trait is wayang spellhunter from one of the dragon empire books.