The first step is you have to WANT to move on.
One of the reasons why people can't seem to "move on" is because they really don't want to move on. You can't get to second base if you insist on keeping one foot on first. Accept that it's over!
Put away old photos into a folder or box, avoid going places you know they frequent. Unfriend or disconnect them from your social media, delete and block phone numbers/email addresses.
Grieve among family and close friends. Focus on hobbies/interests and other things you may have neglected while you were with your ex. Get out and socialize!
Maybe join some hobby/interest groups on Meetup.com or consider signing up with a (reputable online dating site) when you feel ready to date for fun and get to know new people.
Sometimes people are holding out hope for a reconciliation. In other instances they choose to wear "rose tinted glasses" and romanticize the past instead of reviewing the "red flags" and problem issues.
Lastly many people just have complete lack of perspective.
In order for her or him to be "the one" they would have to see (you) as being "the one". At the very least a "soul-mate" is someone who actually WANTS to be with you!
"Never love anyone who treats you like you're ordinary."
- Oscar Wilde
If someone has dumped you or kicked you to the curb they don't feel you were all that "special".
Thankfully there are over (7 Billion) other people!
That woman or man you feel you "can't live without" just know this; There are Billions of people doing exactly just that! In fact you use to be one of us before you got involved with her or him.
Your future lies ahead of you and not behind you.
Every ending is a new beginning!