The word "also" can be used in different ways.
In this case "also" is used to express that sitting somewhere is the logical consequence of whatever was written in the sentences before.
The word "also" might be translated using the English word "so" or "therefore" here.
Normally the word "nun" has a similar meaning than the English word "now" but in texts completely referring to the past it might also mean "after that".
In this case however I think that the word "nun" is manly used to amplify emotions when reading the sentence. (And it has no actual meaning.) "Nun" is sometimes used this way - especially in combination with the word "also".
(However both words may also be used in one sentence describing a pure fact while both words have their "real" meaning.)
To translate the sentence we could imagine the sentence is following that one:
I was very tired so I decided to sit down.
Then the next sentence could be:
Da sitze ich nun also, wie fast jeden Tag ...
... which would translate to:
So I'm sitting there just like every day ...
Please also note that in German the present tense is often used instead of nearly any other tense (especially the future).
Therefore "ich sitze" might also translate to "I sat" or "I will sit".
EDIT about your comments
This sentence begins the story.
As far as "nun" I understood it to be kind of a clarification of "da"
I'm not a literature expert so anything I write in this paragraph may be wrong. But I have already seen such texts.
Maybe (I'm not sure) by referring to a previous sentence that does not exist the writer wants to give the readers the impression that his story starts in the middle of the action and that they do not have to read a lot of boring pages until the "real story" begins.
Just as if the writer wants to say: "I have removed all that boring introduction of the story. You only have to read the interesting part."
The word "nun" belongs to the word "also", not to the word "da":
I myself understand this combination in a way that this sentence is definitely the consequence of something that happened in the text before. So by using these two words at the beginning of the text the writer really wants to give the readers the impression that something has been left out.
so that "da" means "here" instead of "there".
The word "da" can indeed mean both.
However I understand the sentence in a way that the separable verb "dasitzen" (which might be translated to: to sit there doing nothing) is meant.
Note: If this is really true this sentence does not use the official German grammar: The part "da" (of the word "dasitzen") should be at the end of the sentence in this case:
Ich sitze nun also da, wie fast jeden Tag ...
However writers of literature, poems and music lyrics you'll often intentionally do not use "correct" grammar.