Well... the most usual thing would be "push mystr" - put the address of the string on the stack. If you really want the string itself on the stack...
mystr db "1234512345", 0
mystr_len equ $ - mystr
...
sub esp, (mystr_len + 3) && -4
mov edi, esp
mov esi, mystr
mov ecx, mystr_len
rep movsb
...
add esp, (mystr_len + 3) && -4
Not much point in copying the string to a "local" variable, usually, but there might be some reason to do so... What do you have in mind?
Best,
Frank