This whole section is dedicated to learning how to say "if" in Japanese. Oh, if only it was as simple as English. In Japanese, there's four (count them, four) ways to say "if"! Thankfully, the conjugations are sparse and easy especially since you don't have to deal with tenses.
We'll first cover the simplest type of "if" which is the natural consequence conditional. This means that if [X] happens, [Y] will happen as a natural consequence. No question about it. If I drop a ball, it will fall to the ground. If I turn off the lights at night, it will get dark. We can express this type of condition in the following format.
These examples are designed to show how 「と」 is used to express natural consequence. However, even if the statement isn't a natural consequence in itself, the 「と」 will tell the audience that it is nevertheless expected to be a natural consequence.
The "for sure" part is the implied meaning supplied by the 「と」. The speaker is saying that the following condition will occur in that situation, no matter what. As you can see from the last example, if the condition is a state-of-being, it must be expressed so explicitly using 「だ」. This applies to all non-conjugated nouns and na-adjectives as I'm sure you're used to by now. This will also help prevent confusion with other types of 「と」.
Another relatively easy to understand type of "if" is the contextual conditional. You can use this particle to express what will happen given a certain context. For example, if you wanted to say, "Well, if everybody's going, I'm going too" you would use the 「なら」 conditional because you are saying that you will go in the context of everybody else going. The contextual conditional always requires a context in which the conditional occurs. For instance, you would use it for saying things like, "If that's what you are talking about..." or "If that's the case, then..."
In a sense, you are explaining what would occur if you assume a certain condition is satisfied. In other words, you are saying "if given a certain context, here is what will happen." You will see this reflected in the English translations as the phrase "if given" in the examples.
The 「なら」 is attached to the context in which the conditional occurs. The format is the same as the 「と」 conditional, however, you must not attach the declarative 「だ」.
アリス：図書館はどこですか。
Alice: Where is the library?
ボブ：図書館なら、あそこです。
Bob: If given that you're talking about the library, then it's over there.
The following is incorrect.
You can also decide to use 「ならば」 instead of just 「なら」. This means exactly the same thing except that it has a more formal nuance.
The next type of conditional just expresses a regular "if" condition without any assumptions or embedded meanings. The conjugation rules for the 「ば」 conditional is below. Note, the conjugation rule for nouns and na-adjectives is actually using the verb 「ある」 in 「である」, a formal expression we'll learn much later.
I call this next conditional the past conditional because it is produced by taking the past tense and just adding 「ら」. It is commonly called the 「たら」 conditional because all past-tense ends with 「た／だ」 and so it always becomes 「たら／だら」. Like the 「ば」 conditional, it is also a general conditional.
For i-adjectives and verbs, it is very difficult to differentiate between the two types of conditionals, and you can make life easier for yourself by considering them to be the same. However, if you must insist, I searched around the web for an explanation of the difference that I can agree with. Here is the original text. Basically, the 「たら」 conditional focuses on what happens after the condition. This is another reason why I call this the past conditional because the condition is "in the past" (not literally) and we're interested in the result not the condition. The 「ば」 conditional, on the other hand, focuses on the conditional part.
Let's compare the difference in nuance.
Ａ：友達に会えれば、買い物に行きます。
A: We will go shopping, if I can meet with my friend.
Ｂ：友達に会えたら、買い物に行きます。
B: If I can meet with my friend, we will go shopping.
Ａ：お金があればいいね。
A: It would be good, if I had money, huh?
Ｂ：お金があったらいいね。
B: If I had money, it would be good, huh?
Going by the context, the 「～たら」 form sounds more natural for both examples because it doesn't seem like we're really focusing on the condition itself. We're probably more interested in what's going to happen once we meet the friend or how nice it would be if we had money.
The past conditional is the only type of conditional where the result can be in the past. It may seem strange to have an "if" when the result has already taken place. Indeed, in this usage, there really is no "if", it's just a way of expressing surprise at the result of the condition. This has little to do with conditionals but it is explained here because the grammatical structure is the same.
You can also use 「たらば」 instead of 「たら」. Similar to 「ならば」, this means exactly the same thing except that it has a more formal nuance.
Some of you may be aware of the word 「もし」 which means "if" and may be wondering how it fits into all of this. Well, if you want to say a conditional, you need to use one of the conditionals discussed above. 「もし」 is really a supplement to add a sense of uncertainty on whether the condition is true. For instance, you might use it when you want to make an invitation and you don't want to presume like the following example.