In order to edit a page in a Google site you must be logged into Google and have editing level rights for that page.
If you are not logged into Google, when you look in the upper, right corner of the page you are on, it will look something like this:
If you are logged in and you have editing level rights to the page, you will see more options:
If you are visiting a Google site page and want to login, perhaps the easiest route is to look for the diminuative "Login" link listed in the page footer:
Note that if you are logged into Google but do not have editing rights to the page, your view/options will look the same as if you are not logged in at all: