Generally you should not squeeze boils as it can spread the infection. Apply a warm compress to it regularly to encourage it to come to a head so that it will drain. That looks badly infected so you should go and get some antibiotics from your doctor. When it drains it may leave an abscess which should be packed with gauze to encourage it to heal from the bottom upwards. See a nurse if this happens who will be able to show you how to dress it properly.
Once it starts draining you may be advised to gently squeeze the puss out if there is a lot of it, to ease the pain. Your local nurse will be able to advise you. It is however very painful - I suffered from terrible recurring abscesses when I started shift work a few years ago and because there was so much puss, the nurse advised me to do this. She did it the first time and it hurst so much I uttered a rude word in front of her!
It should be done gently to encourage the puss to drain, and so that puss doesn't get forced into the surrounding areas and spread the infection. Your doctor or nurse may decide to lance it when you go to get antibiotics.