"Can I get this one?"
は is a topic marker, meaning it is used to tell the subject of a sentence. を is used in cases of a direct object. If there is a verb that shows a person is doing the action to an object, を would be used.
I'll give you an example. Take the sentence "Tanaka eats rice." In Japanese, this sentence would read, "田中さんはごはんをたべます。" (I left everything in kana except the person's name for ease of reading.) In this sentence は marks the topic of the sentence as Tanaka. を shows that ごはん (rice) is the thing being eaten (the verb たべます).
In the sentence you commented on, there is no explicit verb, but をください is an expression used to say "please give me ___", the blank being the direct object that came beforehand. Here, they used the functional pronoun これ to just say "this thing."
Hope that helps!
I'll try to give you a rough explanation, until someone else can provide a better one.
は is normally used right before an adjective. An example would be これはたかいです。たかい, in this case, means "expensive". The object (これ) is being described as expensive. So, は is used.
を is normally used before a verb, or an implied verb. In this case, ください would be an implied verb, because even though it's normal usage is just "please", in this case it means to "please give me" as the hover translation says. Another example would be これをつかって. つかって means "use", so the speaker is telling the listener to use (verb) the object (これ).
Hope this helps a little bit. This was a fairly weak explanation, so I'm sure you'll be granted a better one, hopefully soon. I would be able to give a better one, but I've picked up the bad habit of forgoing particles altogether, as most natives do in regular speech anyway.
I found remembering the common KSAD construction helpful when learning these! (More here: http://www.japaneseprofessor.com/lessons/beginning/demonstratives-the-ko-so-a-do-series/ )
I really recommend using LingoDeer for all this. Their intros explain all of this and they set it up so well. I have never found it confusing or get them mixed up. So much so I didn't even think about them being easy to mix up until I started Duolingo. Not the best for grammer. However they are a lot better for helping with vocab and kanji.
Maybe I can give a more comprehensive explanation of the ko-, so-, a-, do- prefixes that can help you understand better without knowing the intricacies of the English language.
Ko- (ko/chira/re) refers to something close at hand "within reach/closer to the speaker".
So- (ko/chira/re) refers to something further away "just out of reach/closer to the listener"
A- (soko/chira/re) refers to something far away or "in the distance." Something beyond both the speaker and the listener.
Do- (ko/chira/re) indicates a question (dore: what, doko: where, dochira: polite where/which direction)
User Karen_EMM posted a link that describes the grammar very well.
As Lori said, は is a "topic" marker. Though often it is used for the "subject" of the sentence, the "subject" and the "topic" are not always the same thing. Somtimes something that would normally be an object is made the topic; then は gets used instead of を. Example: "手紙は書きますか。" Is "(About) letters, do you write them?" I wrote in more detail about this elsewhere. I'll post the link when I find it.