You get bonus points for being honest and saying this is a homework assignment. Most noobies come in asking for help on code they are supposedly working on for "clients".
Anyway, let's invoke KISS and not over complicate things atm by worrying about data validation. I'll assume a user won't enter letters in an input that expects a number and vice versa.
The first thing you need to do is get the <form> data into variables in your calculate().
All html elements are objects, and objects can have properties and/or methods (functions) to access or manipulate those properties. id is a common property to most elements/objects.
To access an object you can use the DOM's (Document Object Model) getElementById() method. To access a property of an object you append the property's name with a dot to the object's reference. ie. objectRef.id would return the id of an element.
So, to get the first name entered by the user you could have something like
var fName = document.getElementById('num1').value;
alert('First name = '+ fName); //for testing
Note also, that all inputs are strings even when you enter a number like salary and so they have to be converted to a number in order to do any calulations with them. You can use Number(), parseInt() or parseFloat(). My preference is Number(). To get the salary into a number variable so you can calculate the taxes you cpould do something like this
var sal = Number(document.getElementById('num3').value);
So, have a go at getting the 3 inputs into variables at the top of your function and check them with alert() statements. One you have the form data stored in varibales correctly, calculate the taxes and output the information you need in an alert() at the end of your calculate().
If you need more help, post back.
A couple of side issues.
1) The <center> tag is obsolete and deprecated and so should not be used. There are more appropriate css styles to centre text or whatever.
2) The name attribute in <form> is deprecated and is not needed at all.