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I think I'm missing something here. I thought that land cards that have two colors at the bottom mean that they can be used as land for either of the colors.
Take for example Scalding Tarn:
It looks like it's already a combo island/mountain card. So why would I want to use the activated ability which states:
Pay 1 life, Sacrifice Scalding Tarn: Search your library for an Island or Mountain card and put it onto the battlefield. Then shuffle your library
First of all, as the other answers have indicated, Scalding Tarn does not produce any mana, it just lets you search for another land that can. The colors on this card have absolutely nothing to do with its ability. The blue and red are just there as a visual reminder that the ability lets you search for an Island or a Mountain. The card could be orange, or pink, but the ability would still be the same.
So, down to the real question: why is its activated ability useful, especially since you have to pay a life?
Here are a few benefits/uses:
1) Flexibility
That Scalding Tarn in your hand could turn into, for example, Volcanic Island, Plateau, Underground Sea, or just a basic Mountain or Island. You have the flexibility to search for whatever land you may need to cast stuff.
Let's say in your opening hand you have a Scalding Tarn, a Lightning Bolt, and a Spell Snare. Play the Scalding Tarn, then you can wait to "crack" the fetchland until the last second. If your opponent plays a creature, grab a Mountain to cast Lightning Bolt; if they play a 2cmc spell, grab an Island to cast Spell Snare instead. Flexibility!
2) Synergy
Shuffling: Let's say you play a Brainstorm, and don't really like the cards you put back on top (maybe they're all lands that you don't need). Crack Scalding Tarn to shuffle your library! Better to shuffle hoping that you'll get something worth drawing than to sit there for a few turns knowing you'll draw crap that doesn't help you win.
Landfall: Let's say you have a Steppe Lynx in play. Then play your Scalding Tarn, immediately crack it, and grab some land you need. Two lands entered play, so now Steppe Lynx is a 4/5 monster (for this turn) that only cost you 1 mana and 1 life. Totally worth it. Landfall + Fetchlands can give you some bonkers plays.
Graveyard: By cracking the fetch, you put a card in the graveyard, which can benefit things like Grim Lavamancer/Tarmogoyf/Deathrite Shaman
3) Filtering/Thinning
Every time you search your library for a land, you reduce the chance of drawing a land the next time you draw. This is nice later in the game, when lands are typically dead draws.
Statistically, the "thinning" effect of a single fetchland doesn't make a big difference, but multiple copies can. If you play fetchlands and your opponent doesn't, you'll have a slight edge in terms of drawing potential threats (instead of lands), but at the cost of some of your life.
Remember, cards like Necropotence taught us long ago that life is just another resource; using your resources wisely will win you games. That being said, sometimes the life loss associated with fetchlands may not be wise. Some tournament-worthy decks run 6-8 fetchlands, others run 1-2, some run none at all. It depends entirely upon your deck versus the metagame you've chosen to play in.
IMHO, fetchlands are a much better choice when used for flexibility and/or synergy than for just deck thinning alone, but that's just me. You get the deck thinning automatically, but the flexibility/synergy comes with intelligent deck construction.
Anyway, if you don't want those Scalding Tarns, I'll take them. Aside from being good cards for all of the reasons I've just described, those suckers are worth something like $70 each right now!
I thought that land cards that have two colors at the bottom mean that they can be used as land for either of the colors.
No, the color shown on a card means nothing. It's just a visual reminder of some color(s) the card is associated with in some way.
The only lands that can tap for mana without it being written on them are those which have one or more of the five basic land subtypes: Island, Mountain, Plains, Swamp, or Forest. You need to look for those on the type line, which is in the middle of the card, where it says "Land" - that will be followed by a dash and then the card's subtypes. For example:
Because Steam Vents has "Island Mountain" on the type line, you could tap it for either blue or red mana, even if it doesn't have abilities to do that in its text box. Note that the text at the top of its textbox — ({T}: Add {U} or {R} to your mana pool.) — is not an ability in itself, but just reminder text about the abilities that the "Island" and "Mountain" subtypes give it.
Scalding Tarn is a Land, but it is not a Basic Land. Although colored half blue and half red, it does not actually have the ability to tap for mana. Only lands with a Basic Land Type have the inherent ability to tap for mana, regardless of whether the ability is printed on the card.
305.6. The basic land types are Plains, Island, Swamp, Mountain, and Forest. If an object uses the words “basic land type,” it’s referring to one of these subtypes. A land with a basic land type has the intrinsic ability “{T}: Add [mana symbol] to your mana pool,” even if the text box doesn’t actually contain that text or the object has no text box.
Nonbasic lands, such as Scalding Tarn, only have the abilities that are printed directly on the card. Therefore, to get any mana out of your Scalding Tarn, you have to use its ability, sacrifice it, and find an actual Island* or Mountain*.
*Note that cards like Watery Grave are not named Island, but they have Island as a subtype, and can therefore be retrieved with a Scalding Tarn.
Text box coloration means diddly squat in Magic. Does the text box explicitly list any mana-generating abilities? No. Does the type line (between the art and the text box) explicitly list any of the five basic land types — Plains, Island, Swamp, Mountain, and Forest — which automatically grant a mana ability to the card they're on? No. Thus, the card cannot generate mana on its own, and its only ability is the one printed in the text box.
Text box colors are determined by various aspects of the card, but they do not determine anything — the actual properties of a card are determined by the text and symbols printed on it.
Two words:
Whenever a land enters the battlefield under your control, add 1 mana of any color to your mana pool. Playing a regular land and a mana dork on turn 1 would allow you to play a lotus cobra on turn 2, and proceeding to play a scalding tarn (or one of his friends) to fetch another land and tap that land. Tarn triggers cobra for an extra mana, then the other land triggers cobra for an extra mana, then you tap the new land - suddenly you have 3 mana, two of which are any color, available on turn 2, even though you've already played a 2 drop this turn!!
