Translation:As soon as I go swimming, I am better.
Yes - have you heard about Hauptsatz (independent clauses) and Nebensatz (dependent clauses)? This gives a few examples of why verbs are in different places some times... http://christianlangenegger.wordpress.com/2012/01/15/making-complex-german-sentences-easy-coordinating-conjunctions/ and http://christianlangenegger.wordpress.com/2012/01/22/german-subordinating-conjunctions-yes-sometimes-the-verb-goes-at-the-end/ These rules are taught in level A2 German. In my experience, once you get some proper word order going with a decent vocabulary, people understand you heaps easier in everyday conversation.
You would be right, if what I had said it correctly. Re-reading the sentence, the subject isn't going swimming in the future, but going somewhere to swim.
What I realize now is that clackz does not realize that the "Sobald..." is a subordinate clause and thus the conjugated verb comes at the end of the clause instead of in the normal 2nd position.
Have you learned the phrase "wie geht es dir"? I means "how are you", but literally translates into "how does it go for you", the "it" meaning "life, stuff, things in general". It is a very similar construct, "geht es mir besser" would translate into "it goes better for me", meaning "life, stuff etc" goes better.
The way I understand it is, when the dative pronoun "mir" was used instead of "ich" it changed this sentence to I feel better. For instance, if you wanted to say 'I am cold,' you would not say 'ich bin kalt' as this implies you are a cold (hearted). To say you feel cold, you would use 'mir ist kalt.' I'm sorry I don't have an article for you. It's just something I learned along the way. Maybe someone else will have a more in depth explanation they can add! :)
"Besser gehen" is more like "Have gotten better" and is mostly used with health problems (You can use it with other things too for examples "Es geht mir jetzt besser mit dem Schreiben" "I'm better now with writing" but health Problems are the most common). If you use "besser gehen" always think of it like a review. e.g. you can say "Jede Stunde geht es mir besser" (Every hour I'm getting better) if you're ill. In fact you're comparing how you feel at different times (for example at 10 a.m. you feel very bad, at 11 a.m. better...) and come to the conclusion you're getting better.
If you want to say you're getting better at a particular Task (e.g. sports) you should use "besser werden" or "verbessern"
"Mir es geht besser" ist not grammatically correct, 1) it is subordinate and make the verb go in the first position 2) as the verb is taking the first position, the subject 'es' goes into the second [NOTE: position of verb and subject depends of the subordinate, with sobald it works this way], 3) you need to put the pronoun 'mir' after the subject, pronouns take always the first position available, and as position 1 and 2 are taken, it goes into the third