Help understanding interpretation from Spanish to English
B.Oliver

Regarding your example: "No, es mi libro"
I suggest to read it as "No, es mi libro" - at least after the initial Beginner phase I would simply try to understand the content in the target language.
Don't overthink it - the understanding will come eventually ...
... here is some of my experience with literal translations:
I have started acuqiring spanish by listening to spanish texts while reading the lilteral word-by-word translations (outside of Lingq, by using material that was already prepared that way). For me this was quite useful at the beginning. I naturally got a sense of the structure of the target language and the meaning of the individual words - without actively trying to learn any vocabulary or grammar.
A lot of the spanish language can be made comprehensible in such a way. Yes, some expressions don't have a literal translation - so we have to figure out their meaning somehow - however I think the literal tranlsation should not hurt in such cases.
Soon after I started to use LingQ for Spanish and never used any literal translation for spanish again. I did not feel I would need this crutch beyond the initial beginner phase.
Since I already know languages that are rather closely related to Spanish (English and French) I think I could have done just fine without the literal translation - however I think it was still useful for me.
Regarding thinking in the target language: It seems to me that thinking in spanish can come gradually and naturally, when we get to a higher level - just like speaking.
If you want to speed up this process here is a hypothesis:
'We will naturally start to speak and think in the target language sooner, when we acquire the language by using more repetitions of the same limited content, rather than just consuming a lot of new content.'
(Note: I don't claim that a lot of repetition is the best way of acquiring the language faster for everyone - this hypothesis is merely about 'triggering' the natural process of speaking and thinking in the target language).
xxdb

Other posters are describing it accurately. It's not just word to word but also collocation and phrase to phrase.
An example: there is a phrase in Mexican Spanish (don't know if it exists in Castilian Spanish) which is "Me caes bien gordo".
Word for word it translates as me you fall good fat.
i.e. gibberish
But in the context of usage you can see it's actual meaning is something like "you are a dreadfully annoying person".
End result, from that example (and other similar examples) you will find out that there are word grouping that describe a situation that do not have a word for word translation but mean the same thing. Conceptually they are the same but syntactically and lexically they are not.
So to answer your question of "how do I get there from here", for me I watched tons and tons of telenovelas where I could *see* the situation and the context and be able to use the Spanish they were using as "labels" for the situation. Anyhow that's how it felt to me.
PeterBormann

"I want to learn to "think" in Spanish but have no idea How a Spanish speaking native thinks as they are speaking."
No human being has the ability to know what another human being "really thinks" (while surfing the associative networks consisting of language and other media forms).
If you want to become native, you have to know thousands of the most common "collocations" (= highly conventionalized word groups). In English, for example:
- get in the car
- get out of the shower immediately
- get up
- get down
- get going
etc.
Unfortunately, native speakers know several tens of thousands of such collocations. And that's why language learners usually "never become truly native".
However, the more collocations you know (by reading / listening / speaking and writing and by using artificial SRS such as Anki), the less you have to translate from your mother tongue into your second language...
Hagowingchun

If you want to think in Spanish you need to acquire a level where the structures and words have equivalents in English but you don't use them when you speak/write. As for listening/reading when you don't know the words this type of translation has to happen to make sense of it, but quickly as you read something where you know all the words no translation has to occur. You now know all the words as separate slots in your brain and whether you know the equivalent of that doesn't really matter unless you care about it specifically.
your example:
una hamburguesa doble con queso y tocino
when you start it will be as if the english words are underneath, but as you get better and know all the words there will be 0 processing time and then once you hear or see "una hamburguesa doble con queso y tocino" your brain will process it for meaning and it wont even have to use English as a bridge. Sometimes you might think about what it would be in English but this is more of a passive double checking that sometimes happens. Sorry if I made this more complicated. Suerte con tu espanol! Hasta luego.
benscheelings

I think punctuation makes the difference:
No es mi libro - It is not my book.
No, es mi libro! - No, it is my book!