The simplest and proper way to do this would be to create new module and in installation method of this module insert code:
Utils_RecordBrowserCommon::new_record_field('contact', <field name>, <field type>, <visible when browsing - true/false>, <field must not be empty - true/false>);
This will allow you to create field of simple type (number, text, date). For more specific fields (Contacts, Companies etc.) you'd need to look up other possible parameters for this function.
Alternatively, you could insert new row in contact_field SQL table with all parameters specified similar to what I described above. However, this solution is not recommended due to possible compatibility issues.
I can provide more details regarding creating particular fields if you specify precisely what kind of field you need.
Kind regards,
Arek