Word Order in Japanese

This is one reason particles are so handy. As long as every part of the sentence is properly marked with particles (where needed), any part can go anywhere as long each part remains intact and the verb goes at the end of the sentence. Even the "verb at the end" rule is sometimes broken in casual speech, though usually only for emphasis or when adding afterthoughts. Generally speaking, the later in the sentence something appears, the more important it is. In any case, all of the following examples are perfectly legitimate (though some are unlikely or even awkward) and while they may put different amounts of weight on the different parts of the statement, all mean the same thing: "I will eat breakfast at nine o'clock tomorrow."

「明日九時に私は朝ご飯を食べます。」 (Ashita kuji ni watashi wa asagohan wo tabemasu.)
「明日九時に朝ご飯を私は食べます。」 (Ashita kuji ni asagohan wo watashi wa tabemasu.)
「明日私は朝ご飯を九時に食べます。」 (Ashita watashi wa asagohan wo kuji ni tabemasu.)
「明日私は九時に朝ご飯を食べます。」 (Ashita watashi wa kuji ni asagohan wo tabemasu.)
「明日朝ご飯を九時に私は食べます。」 (Ashita asagohan wo kuji ni watashi wa tabemasu.)
「明日朝ご飯を私は九時に食べます。」 (Ashita asagohan wo watashi wa kuji ni tabemasu.)
「九時に明日私は朝ご飯を食べます。」 (Kuji ni ashita watashi wa asagohan wo tabemasu.)
「九時に明日朝ご飯を私は食べます。」 (Kuji ni ashita asagohan wo watashi wa tabemasu.)
「私は明日朝ご飯を九時に食べます。」 (Watashi wa ashita asagohan wo kuji ni tabemasu.)
「私は明日九時に朝ご飯を食べます。」 (Watashi wa ashita kuji ni asagohan wo tabemasu.)
「朝ご飯を明日九時に私は食べます。」 (Asagohan wo ashita kuji ni watashi wa tabemasu.)
「朝ご飯を明日私は九時に食べます。」 (Asagohan wo ashita watashi wa kuji ni tabemasu.)
「九時に私は明日朝ご飯を食べます。」 (Kuji ni watashi wa ashita asagohan wo tabemasu.)
「九時に朝ご飯を明日私は食べます。」 (Kuji ni asagohan wo ashita watashi wa tabemasu.)
「私は朝ご飯を明日九時に食べます。」 (Watashi wa asagohan wo ashita kuji ni tabemasu.)
「私は九時に明日朝ご飯を食べます。」 (Watashi wa kuji ni ashita asagohan wo tabemasu.)
「朝ご飯を九時に明日私は食べます。」 (Asagohan wo kuji ni ashita watashi wa tabemasu.)
「朝ご飯を私は明日九時に食べます。」 (Asagohan wo watashi wa ashita kuji ni tabemasu.)
「九時に私は朝ご飯を明日食べます。」 (Kuji ni watashi wa asagohan wo ashita tabemasu.)
「九時に朝ご飯を私は明日食べます。」 (Kuji ni asagohan wo watashi wa ashita tabemasu.)
「私は朝ご飯を九時に明日食べます。」 (Watashi wa asagohan wo kuji ni ashita tabemasu.)
「私は九時に朝ご飯を明日食べます。」 (Watashi wa kuji ni asagohan wo ashita tabemasu.)
「朝ご飯を九時に私は明日食べます。」 (Asagohan wo kuji ni watashi wa ashita tabemasu.)
「朝ご飯を私は九時に明日食べます。」 (Asagohan wo watashi wa kuji ni ashita tabemasu.)

And that's not even taking into account the possibility of also listing where, with who, or other potential details. Generally speaking, the ordering tends to be approximately: Topic, time, place, indirect object, direct object, and of course the verb comes last. However, there are no fixed rules. In casual speech, things may even come after the verb.

「今行く、授業に。」 (Ima iku, jugyou ni.) = "I'm going now, to class."

Noun Modification

Phrases and words that modify nouns come before the noun they modify. In English, qualifying phrases normally come after the noun while adjectives come before. Japanese places both before the noun. In Japanese, the qualifying phrase can be as simple as a brief adjective or as complicated as a full sentence.

If the modifier ends in a short form verb or -i adjective, just place it before the noun, with no further modification. Verbs used to have a special form for this, but it's now obsolete and only appears in old or poetic text, and I'm not sure how to conjugate it in any case.

「黒いＴシャツを着っている人」 (kuroi TIISHATSU wo kitte iru hito) = "person who is wearing a black T-shirt"
「昨日買ったビデオ」 (kinou katta BIDEO) = "video that I bought yesterday"
「青い空」 (aoi sora) = "blue sky"

Modifiers that end in a -na adjective or nouns vary. If the phrase is in negative and/or past forms, then it actually ends with a form of the copula, which is almost a verb and acts as described above.

「先生だった人」 (sensei datta hito) = "person who was a teacher"
「賑やかじゃない道」 (nigiyaka ja nai michi) = "street that isn't busy"

Otherwise, it's a bit different. For -na adjectives, add な (na) between the adjective and the noun. This is why they're called -na adjectives...

「きれいな海」 (Kirei na umi) = "beautiful ocean"

For ordinary nouns, add の (no) in most cases...

「日本人のみちこ」 (Nihon jin no Michiko) = "Michiko who is Japanese"
「会社の車」 (Kaisha no kuruma) = "company car" or "car that is the company's"

...however, there are a few cases where the noun being described is the noun describing it, but using の may suggest a different meaning. In these cases, you can use である (de aru) instead. Here's an example from Chrono Trigger:

「王女である前に一人の女の子なの！」 (Oujo de aru mae ni hitori no onna no ko na no!) = "Before I'm the princess, I'm a girl!"

The meaning could be drastically different if she had used の instead of である:

「王女の前に一人の女の子なの！」 (Oujo no mae ni hitori no onna no ko na no!) = "In front of the princess, I'm a girl!" or "A girl's in front of the princess!"

The first meaning is still possible, but is less obvious without proper context. Using である rather than の here makes it unambiguous.

Particle Placement

Particles must come directly after the word or phrase that they modify, otherwise it's impossible to tell what they're supposed to be doing. This is particularly important to remember with particles that are frequently translated as though they were words, like も (mo), often rendered as "also" or "too", and から (kara), similar to "because". For example, in English, both of the following are valid:

"Mary speaks English. Robert also speaks English."
"Mary speaks English. Robert speaks English too."

However, in Japanese, while this is correct...

「メアリーは英語を話す。ロバートも英語を話す。」 (MEARII wa eigo wo hanasu. ROBAATO mo eigo wo hanasu.)

...the following is not correct:

「メアリーは英語を話す。ロバートは英語も話す。」 (MEARII wa eigo wo hanasu. ROBAATO wa eigo mo hanasu.)

What that actually says is that Mary speaks English, and that Robert speaks English in addition to some other language.

This sentence is even worse:

「メアリーは英語を話す。ロバートは英語を話すも。」 (MEARII wa eigo wo hanasu. ROBAATO wa eigo wo hanasu mo.)

I'm not sure what (if anything) that would mean to a Japanese speaker, but it's certainly not likely to be the intended meaning.