The different particles used with 決める
can express slightly different meanings. Just as in English there may be some overlap in how you can use them, but here are the primary functions of the particles as used with 決める.
(1) ~を決める
を marks the direct object of 決める. It merely tells us that something is being decided (without necessarily explicitly stating what the outcome of the decision was).
小説のタイトルを決めた。
I decided the title of the novel.
In this sentence you aren't saying what the title is, only that you have decided what it is. The title is the object of the deciding-action, hence it is marked with を.
会議の日を決める
to decide the date of the meeting
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(2a) ~に決める
に is used to specify what the outcome of the decision was. Whereas を simply told us that a decision is being taken about something, に is used to supplement that information by explicitly stating what the result of the decision is. In other words, に marks the stated/named end result of the decision.
小説のタイトルを「ぼっちゃん」に決めた。
I decided on "Bocchan" as the title of the novel.
会議の日を23日に決める
to decide on the 23rd as the date of the meeting
(2b) ~に決める
に can also be used to mark the time at which a decision is made. This is a standard use of に which is unrelated to your specific question. But for example:
今日中に決める
to decide today
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(3) ~と決める
と is a quotative particle which tells us the content of whatever verb it is used with. ~と言った tells us the content of what was said. ~と思った tell us the content of what was thought. Likewise, ~と決めた tells us the content of what was decided (and it is expressed as a predicate when used with と).
小説のタイトルを変えると決めた。
I decided to change the title of the novel.
会議の日を変更すると決める
to decide to change the date of the meeting
This time, と is marking the clause which is reporting the content of the decision (expressed as one complete phrase).
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To sum up, you can loosely define the different usages in English as follows:
~を決める to decide (something like a day, a time, etc.)
~に決める to decide on (a named outcome like a specific day, time, etc)
~と決める to decide to (+ predicate with contents of decision)