Can't tell what you did wrong from here.
What you can try:
Open Manage | Database | Fields and select your original table. Add a new field of type calculation. In the specify calculation dialog, select your new, related table from the drop down just above the list of field names. If it's there and listed as related, you can select it and see the list of fields for that table appear below it. Set up your calculation and when you want to add a field, double click its name in the list to get the correct syntax.
If it's not in that drop down list, then it's not related as you thought. In that case, I suggest uploading a screen shot of the relationships so that we can look for possible problems.
kinda works now
How can I make it so that when I add a new record in Products, I can either select a Category or type in a new one, and be assurred that the category will exist in the related field in the categories table. Also, is it possible that the related field in the categories table would be deleted if all the records in the Product field of the particular category are deleted?
Thanks in advance
There are a number of methods that could be used. The simplest is to add a button that takes you to a layout base on your table of categories. Create a new record, enter the category name and then return to your product layout to select this new category. Buttons can switch you between the two layouts for this purpose.