Most Helpful Guy
Relationship is a funny thing. While you may not realise, but you've let the person take up a large space in your mind. Moving on means that you will need to fill the void left by the person.
Don't rush. Time heals the pain. It will take awhile before you realise you are not thinking about that person. That's what's needed.
Keep busy. Remember, you need to fill the void. That means you filling the void with other things. Get involved in various other activities. Take on a hobby. Do volunteer. Travel. Study a new language. Meet new people. The world is big and you haven't met enough people yet.
As you keep yourself busy, you will fill the void and eventually, the time will take good care of you.
Most Helpful Girl
Definitely try to move on on your own. If you just find someone else to fill the void you'll never truly move on and you'll forever harbor feelings for this person.
The thing that helped me most was to hate the person. I know it sounds harsh after a breakup when you still have feelings and miss the person, but trust me it's the best way to go about it. The hate will eventually subside to a point where you no longer hate that person, but you are over them and have no feelings for them anymore. But hating them first is what helps you detach and helps you move on.
And while you're busy hating that person, you should keep yourself busy with other things. Things to make you feel better. Take care of yourself. Eat healthy, work out, go shopping, take a vacation. Do something fun and nice for yourself. If you have some girlfriends that you love being around, hang out with them. Just whatever you like. And when you are ready for a new relationship and you know you are over this, then you can start dating again.