Is it correct to say or write an student or an store?
Always use an for words which sound like they start with a vowel, and always use a for words which sound like they start with a consonant. The rules for h are more complex, and it can be ok to use either.
The usage of the indefinite article preceding h are discussed here. In particular, look at nohat's response.
As for student and store, they should always be preceded with a and never with an, because they both start with the consonant /s/ when spoken.
A student, a store
An student, an store