I am on Livemocha and it says that 買います。 means "I am going to buy it." But I figure that should be 買いに行きます。 . Also I know that ぎゅうにゅうを買っています。 is "I am buying milk." But for some reason, I thought that ぎゅうにゅうを買う. could also mean "I am buying milk." In short, I'm confused about when/how to use which conjugation for what.
The basic form in Japanese like 買う・買います actually means both present tense and future tense. The exact tense depends on usage. For example: 毎日ぎゅうにゅうを買います(I buy milk everyday)・これからぎゅうにゅうを買います(I am going to buy milk) are using different tenses despite using the same 買います.
The difference between 買います and 買いに行きます is not on tense, but on the focus. 買います focuses on the action of buying while 買いに行きます focuses on the action of going (out). In most cases they can mean the same thing but in some cases no. For example: ネットで株を買います(Buy stocks online) will never be said as ネットで株を買いに行きます, as there is no "going out" action involved.
The difference between ぎゅうにゅうを買っています and ぎゅうにゅうを買う is that the first one is present continuous while the second one is in future tense. A proper translation would be "I am buying milk now" and "I am going to buy milk"
Sorry for the long answer.
You are confusing two English sentences: "I am going to buy it" can mean a future form of "buy" (similar to "I will buy it"), or it can be a compound sentence whose main verb is "go" (similar to "I am going out, in order to buy it"). The former is 買う or 買います (which is the same as "I buy it", the plain present tense, in Japanese), and the latter is 買いに行く or 買いに行きます - notice how this contains the verb 行く, "to go". 買っている or 買っています is a sort of continuative present form, and means "I am buying it".
(Actually, the distinctions between 買う and 買っている are a little subtler than that - you can't expect English and Japanese to correspond precisely - but I think the simplified explanation above is enough to answer your question.)