The basic structure is (Topic)(Subject)(Verb)...
ex. (T)Watashi wa (S)Shane (V)desu / I Shane Am --/-- I am Shane....
Actually it's SOV, subject, object, verb. In the case of your example, 私 (watashi) is the subject, Shane is the object, and です (desu) is the verb.
It does a lot of things actually, topic marker is only one of them. It can also be used as a contrast marker.
EX: カナダにならことがありますが、メキシコには行ったこ とがありません。(Canada ni nara itta koto ga arimasu ga, Mexico ni wa itta koto ga arimasen)
"I've only ever been to Canada, not Mexico."
Ga - Marks Subject, "The", "But", and connects nouns
ex. Kirei yama - pretty mountains
Yama (ga) kirei desu ---- Mountains (the) pretty are ---- (The) mountains are pretty
ex. Okii Ie (Big House) ------------ Ie (ga) okii desu - (the) house is big
Perhaps this is just personal opinion, but I think it's dangerous to think of が(ga) as translating to "the". In English, "the" is the definite article, and Japanese lacks the definite and indefinite ("a" in English) articles. Also, honestly, は(wa) could replace が(ga) in these examples (especially since they have no context).
ex. Inu wa suki desu (ga) neko wa kirai desu / I like dogs (but) I don't like cats
好き(suki) and きらい(kirai) are interesting adjectives, firstly because in English their equivalents are verbs. Also, the object that you like or dislike is marked with が(ga).
犬が好きですが、ねこはきらいです。(inu ga suki desu ga neko wa kirai desu) (the は (wa) in the second part is being used as a contrast marker)
No - Possessive Marker
ex. [Watashi wa (no) name]Shane desu / [My name] Shane is --/-- [My name] is Shane
This too has multiple uses (my favorite being its nominalizing function). You do have an error in your example however, it should be:
私の名前はシェーンです。(watashi no namae wa Shane desu)
私の名前(watashi no namae) is a complete noun phrase which acts as the topic / subject in this sentence.
What is nominalization you ask? It lets you say things like:
読むのが好きです(yomu no ga suki desu)
"I like to read."
To - And
ex. Doko Johnny-san (to) Shane-san desu ka
Where Johnny (and) Shane is --/-- Where is Johnny (and) Shane?
Also, "with" and many other functions (I'm going to stop saying that...they ALL have myriad functions).
You use it correctly, however the format of your sentence is incorrect.
It should be: ジョンニさんとシェーンさんはどこですか。(Johnny-san to Shane-san wa doko desu ka)
Just remember that Japanese doesn't invert its sentences like English does when a question is asked (there's a better term for this, but I can't recall at the moment).
English:
"My name is Shane"
becomes
"What is your name"
as a question
Japanese:
私の名前はシェーンです。(watashi no namae wa Shane desu)
as a question is:
あなたの名前は何ですか。(anata no namae wa nan desu ka) (あなた(anata) simply used for illustrative purposes...do not use in real life in most situations)
Ni - In / At / Toward
ex. Gakko (ni) desu --/-- School (in/at) I am --- I am in/at school
ex. Gakko (ni) ikitte desu ---/--- School (to) going I am - I am going to school
Specifically, when talking about the location of something's existence, you don't use です(desu), you use ある(aru) (for inanimate objects like books), and いる(iru) (for animate objects like people).
So, "I am at school", would be 学校にいます(gakkou ni imasu).
Also, you conjugated 行く(iku) incorrectly, the て(te)-form of 行く(iku) is irregular, being simply 行って(itte). Also in this example, you need to use the progressive form of the verb, て(te)-form + いる(iru), not です(desu).
The sentence should be: 学校に行っています(gakkou ni itteimasu)
De - In / At or By
ex. Watashi wa gakko (de) neru -/- I school (at / in) sleep --- I sleep (at / in) school
ex. Jitensha (de) ikimasho --/-- Bicycle (by) let's go ----- Lets go (by) bycycle
Good, no problems here (except you forgot the long vowels in 学校(gakkou) and 行きましょう(ikimashou)).
E - Toward
ex. Gakko (e) ikitte desu -- School (to) going I am -- I am going (to) school
ex. Nihon (e) yokoso ---- Japan (to) welcome --- Welcome (to) Japan
Yep, pretty much the same as に(ni) in this usage, though don't forget what I said about 行く(iku) and progressive form.