Log into your BigCommerce Admin Account. Choose "Advanced Settings" in the lower part of the left navigation bar of your screen.
Choose "Live Chat" in the left navigation bar, then select "Other Third Party Live Chat Service" from the available options and click "Save".
Select the tab "Other Third Party Live Chat Service" next to the "General Settings"-tab. Paste the Userlike Widget Code in the box and hit "Save”. You're all set up.
If your Userlike Chat Widget does not appear in your shop, try another "Chat Box Location". In general, different BigCommerce themes can interfere with 3rd party plugins, see this thread in the BigCommerce support forum.