It sounds to me like you may be having trouble understanding how to add php, not just how to add a form. The Joomla UI is a UI for end users it's not one for developers. For adding a form you need to have a way to get the form into the UI. That's why people have probably recommended that you use a forms extension, because those provide a simple UI for doing so.
How you make the form is going to depend on what you are doing with it and whether you want to save to the database i.e. is it a search form, a filter in the back end UI, or creating content that you want to save.
Do you want to insert this form inside an article? Or do you want it to be its own separate thing that would have a menu item?
So, for any kind of proper Joomla code you need to make an extension, and in your case I would guess it is probably appropriate to make a plugin. You can use the profile plugin as a model if you want.
In your plugin the way I usually would do it (after doing the usual content plugin work of identifying the event and context and so on) would be to define my fields and fieldsets in an xml file.
Then in your php you would instantiate a JForm and echo out the labels and values the way it is done in all the core forms (i.e. look at the article edit layouts).
Without knowing more about the context and purpose of your form it's hard to give more detailed advice than that. I don't want to put links to docs that are going to just be frustrating for you.