It will be the same as you insert a record into the database.
The only difference will be you will use "UPDATE" instead of "INSERT", and you need "Where..." parameter in order to find out exact record you want to update, and apply the command.
The whole process will be like this:
Collect all the data in the form, and pass it to another ASP script file that contains following SQL query string. "UPDATE field name1, field name2... value(value1, value2...) where keyfieldname=value"
Of course, you may want to check the data that was input by the user before update to see if all the data is in the right format. Because almost no one wants to users to destroy their application and database by entering some bad data in it.
Good Luck!