The easiest would be as Chris suggested and simply use a hidden form to submit with API_AddRecord or you can use an AJAX post method to do the same. To find the field ids to reference you can look at the fields in your QB and, if I remember correctly, you can find an advanced button and have it show you the field ids in the listing as well.
Once you do that, you'll be able to find your field ids to associate correctly and use a form or the api to add the record.
https://help.quickbase.com/api-guide/index.html#add_record.html%3FTocPath%3DQuick%2520Base%2520API%2...
