What do you mean, time, manner, place?
In English, the order of adverbs isn't an important consideration. You can say, "Next Tuesday, I'm going to the mall," or you can say, "I'm going to the mall next Tuesday." Emphasis comes from the way we say words in English, and placement in a sentence isn't all that important.
In German, though, things are a little bit different. The conjugated verb (in other words, the verb that changes to suit the subject) always takes the second position in a German clause. The Germans refer to the concept this way: verb an zweiter Stelle (verb in second position).
What does this mean? Well, in a simple sentence this is easy.
English: Dirk is at school today.
German: Dirk ist heute zur Schule. Notice: "today" comes before "at schoo" in the German sentence. We'll come back to this.
What about when there's a helping verb or a modal verb? Remember — the conjugated verb stays in the second position, while the action verb goes all the way to the end of the clause.
English: Frieda is supposed to eat with us tomorrow.
German: Frieda soll mit uns morgen essen. The action verb, "to eat," goes to the end of the clause.
Where does Time, Manner, Place come into all of this? Well, because the action verb won't come until the very end of the clause, in a lot of cases, the reader (or listener) can get confused as to what is going on, and so in German, you write (and speak) adverbs in the order of time, manner, and place. This includes adverbial phrases, such as prepositional phrases.
So how does this look?
"Time" and "place" are pretty easy to figure out: when and where things happen. "Manner" describes how they happened, or the way in which things happened. Here's an example:
Last period, the students ran to the gymnasium loudly. "Last period" tells us time, "to the gymnasium" tells us place, and "loudly" describes the manner.
And so in German, the sentence would read like this: Die Studente sind letzte Stunde unruhig in die Turnhalle gelaufen.
Unruhig is one way to say "loudly." Note the ordering of the adverbs and adverb phrases.
Are there any exceptions?
Of course there are — otherwise, language learning wouldn't be so fun, right?
Let's say that there is one particular adverb that you want to emphasize. Maybe you are arguing with your parents where you were last night. If you want to tell them, "I was at the library last night," when they think you might have been clubbing, you would say:
"In der Bibliothek war ich gestern Abend!" instead of "Ich war gestern Abend in der Bibliothek!"
Notice that the subject has moved to the other side of the verb — this is because the conjugated verb always takes the second position in a sentence. The expression of place comes before time and manner, but it's for the purpose of emphasis.
You can also move expressions of time and manner in front of the verb if you want to emphasize those. If the subject is the first word in the sentence, though, or if you are asking a question, always order your adverbs and adverbials correctly — it will help your audience understand you.