An embedded upload form sits on a page of your own website, so people upload without ever leaving your site. It is the same form as the one on your share link, with the same fields, the same upload destination, and the same submissions. Embedding is available on the Business and Premium plans.
The form has to be published before an embedded copy will work. See Form statuses.

The code you copy is a single snippet with two parts: an iframe that holds your form, and a short script that resizes the iframe as the form's height changes. Paste it whole. Without the script the form sits in a fixed box 600 pixels tall, which is shorter than most forms need.
On the Starter plan the Embed Code section is dimmed behind a padlock, above a line reading "Embed codes are available in Business and Premium plans."
Three switches sit above Copy Embed Code, and all three start on.
Set them before you copy. They are written into the code at the moment you copy it rather than saved on the form, and they go back to on the next time you open the tab. Changing them later means copying the code again and replacing what you pasted.
Turning all three off leaves the fields, the File Upload area, and the submit button on their own. That is usually what you want when the page around the form already carries your logo and explains what to send. What is left still carries the form's colors, font, and styling. See Style your form.
Preview opens an Embed Preview window showing the form as your switches have it, so you can check the result before touching your site.
It previews the display switches only. The password screen and the CAPTCHA are both skipped in it, so a password-protected form shows its fields here and still asks for the password once it is embedded for real.

Paste it into whatever your site builder calls a code element, at the spot where the form should appear, then save and publish that page. A normal text block will show the code as text instead of running it.
Anything else that accepts raw HTML works the same way. Some builders put your code inside a frame of their own with a height you set, and a form that is cut off in one of those needs that frame made taller.
WordPress has one catch. The Custom HTML block works on self-hosted WordPress and on WordPress.com plans that include hosting features, which starts at their Business tier. WordPress.com's Free, Personal, and Premium plans strip iframe and script tags out, so an embedded form will not appear on any of them.
The form measures its own height and passes it to the page around it, and the script you pasted resizes the iframe to match. That is what stops the embedded form scrolling inside its own box as fields appear and files are added.
The iframe starts 600 pixels tall and no more than 600 pixels wide. Both numbers are plain HTML in the code you pasted, so you can change them. Widening it is safe: edit or remove max-width:600px in the iframe's style. The height is set by the script whenever the form's height changes, so editing the starting height only affects the moment before the first measurement lands.
If the script never reaches the page, the iframe stays at 600 pixels and the form is cut off rather than scrolling, because an embedded form turns off its own scrollbar. A form that looks cut off usually means the script did not survive the paste, or something on your page is blocking it.
An embedded form behaves almost exactly like the form on its own share link. Uploads are delivered to the same upload destination, submissions land in the same place, notifications send the same way, and file organization works the same. Four things are worth spelling out.