I would suggest you to just take the [2-minutes-tour on Ask Ubuntu](https://askubuntu.com/tour). It describes the most important things on how the site works supported with some nice images and provides you all useful links you might want to visit for a better understanding of the site.

To briefly answer your personal questions:

- You thank the person that answered your question best by accepting his/her answer (click on the gray tick next to the answer so that it becomes green). Beware that you can only accept one answer per question and only accept answers to your own questions. This will earn the poster +15 [reputation](https://askubuntu.com/help/whats-reputation) and give you yourself +2 reputation points.  
- You can also upvote his answer by clicking on the gray arrow upwards next to the question. This gives +10 points to the poster, but requires you to have at least 15 reputation points. Though, you can vote on questions AND answers of everybody and everywhere. The only restriction is that only one vote per post is allowed, but e.g. you can vote on two answers to one question.
- The people in here who try to solve others' problems are also just humans, so except from collecting reputation points, you also can make them happy by leaving a short friendly comment on their posts. Note that below 50 points of reputation, you only may write comments to your own posts and on answers belonging to your questions.
- Of course you can post as many questions, answers and comments as you want and we are happy about everybody who participates actively on Ask Ubuntu! Only make sure that you avoid duplicates whenever it is possible. So: Use the search function to look for Q&As that already might solve your problem before writing a new question and read other people's answers and comments before you write one yourself.

I hope this answers your information request on AU. Feel free to try the thanking options at this answer (although no reputation will be awarded on a Meta question). If something is still unclear, you can try out the comment function and leave me one here :-D  
_Greetings and enjoy AU!_