Unless the website itself includes that information, there is no way of figuring out when a page was last updated that is always guaranteed to work. You may get lucky and find a precise date, but you may also be only able to make an educated guess or find no information at all.
With the web page in question open, type or paste the following text into your browser's address bar, replacing whatever is there, and press Enter:
In response, the browser prompts you with the date and time the page was last modified, according to the server that hosts it. This method is not guaranteed to be accurate, especially not in the case of dynamically generated pages. Even if the page in question is a static one, the date may simply be when it was restored from a backup or when its layout was changed, rather than when its content was updated.
Enter the page's address into the Wayback Machine and look through the list of results. You can use the results to get a general idea of how recent the content is, although most websites aren't indexed regularly, so you won't be able to get an exact date; also, some websites aren't indexed by the Wayback Machine at all, for a variety of reasons ranging from the site owner requesting its exclusion to the way the site was built.
Video of the Day
Check the address for the page, as well as the HTML source for it. Depending on how it was built, it may use a date as part of the address for the page itself (http://www.example.com/2015/01/23/page.html) or for other files included in it (http://www.example.com/images/20150123.jpg), or have a date string as part of the code. This date is more likely to be the date the page was created than the date the page was updated, but it can still give you a general idea of the page's age.
Look through the page's contents for any clues that might help you place it in a rough timeline. These clues usually come in the form of a reference to a particular date and can range from extremely specific to very vague. For example, the birth of Prince George of Cambridge could be referred to as happening "three days ago," "a few weeks ago," "last month" or "two years ago" -- in all cases, the information helps you roughly date the page, but the level of precision varies.
Contacting the Owner
The last resort to find out when a page was last updated is to get in touch with the owner -- most websites include a contact method, usually email or a contact form. You are not guaranteed an answer, however, and the older the website is the lower your chances. The contact method may be out of date, the website may be completely abandoned, or the owner may simply neglect to respond.