The first people you should notify are your parents.  If it is at all practical and/or possible, you should let them know in person.  If it is not possible due to distance or timeliness, then a phone call with both you and your fiancée there to share the news is the next best option.

Close relatives and friends can be informed in person or by telephone.

Others can be informed in any way  desired: person, phone, e-mail, or regular mail.

An engagement party is a fun way of informing relatives and friends of the exciting news.  If you choose to have a formal engagement party, fully catered,  it can also be a great way to try out a catering service before the wedding.

After your close relatives and friends have been notified, you may consider a formal announcement of your engagement in your local newspaper and in the parents' hometown newspapers (If they are out-of-town).

Newspaper Announcement of Engagement

You may include a photograph along with a write-up.   Your official engagement should be announced within one year of your wedding date.

Having engagement photos taken by a potential wedding photographer can be a great way to immortalize the occasion, try out the photographer, and acquire a photograph for the newspaper announcement.

Some newspapers have special forms to fill out for the announcements.  Check the newspapers that you plan to place your announcement for their requirements so you can be prepared.