The word 'also' is called a disjunct adverb, meaning that it carries extra information. Notice the commas (,...,) in the example sentences below. Disjunct adverbs modify the verb as well as the entire sentence, so they can move around freely among the constituents:
She, also, is going to the store. She is, also, going to the store. Sheis going to the store, also.
It's difficult to say which of the above is the most natural form because speaker us(ag)e is related to speaker choice. But, if we look at the constituents that make up the sentence, then it seems speakers like to place the adverb outside of the constituents [...], like this,
[She], also, [is going to the store].
[She] [is going to the store], also.
But, please note, "She is, also, going to the store" is OK, too. In that case, the Verb constituent "is going" is viewed by the speaker as two units within one constituent:
I find that I use "She, also,..." when I want to place emphasis on the subject, and that I use "She is, also,...." when I want to place emphasis on the event. More often than not, though, I tend to use "..., also" as a means of covering both bases.