Breakups. They hurt.
I believe it is important to feel the pain, rather than distract from it; to realise it is OK to feel like this. In fact, it is better than OK:
"Heartache reminds us that people aren't disposable. Every person we share ourselves with should be someone special, or we made a mistake." - Steffi Schnobel
The pain now means that the person in question touched our heart. There was a profound connection, and that is a beautiful thing. Bring your attention inward: breathe deeply, feel the tears roll down your cheek, put a hand on your heart and feel it hurting, but notice that it is still beating.
"Every person we meet touches us and adds to us in a unique way. Try to focus on what their role in your journey was, and what you were for them." - Steffi Schnobel
There is something to be learnt from every experience. Switching to a gratitude mindset, rather than focusing solely on the pain will help you to sleep, and then to eventually move on.
"There is no remedy for love but to love more" - Henry David Thoreau
Send the person in question, and yourself, some loving kindness.
Plan to do some activities you enjoy. Reach out to your friends and other people you love. Along with hugs and stories of their own struggles, they can give you advice (thanks, Steffi). Go outside, do some gentle movement/exercise, meditate, listen to music, draw, have dinner with a friend -- whatever you need to give you an extra boost.
Compassion and kindness, towards yourself and others, is always the key to healing.