How to change TextField’s height and width?

To adjust the width, you could wrap your TextField with a SizedBox widget, like so:

const SizedBox(
  width: 100.0,
  child: TextField(),
)

I’m not really sure what you’re after when it comes to the height of the TextField but you could definitely have a look at the TextStyle widget, with which you can manipulate the fontSize and/or height

const SizedBox(
  width: 100.0,
  child: TextField(
    style: TextStyle(fontSize: 40.0, height: 2.0, color: Colors.black),
  ),
)

Bear in mind that the height in the TextStyle is a multiplier of the font size, as per comments on the property itself:

The height of this text span, as a multiple of the font size.

When [height] is null or omitted, the line height will be determined
by the font’s metrics directly, which may differ from the fontSize.
When [height] is non-null, the line height of the span of text will be a
multiple of [fontSize] and be exactly fontSize * height logical pixels
tall.

Last but not least, you might want to have a look at the decoration property of you TextField, which gives you a lot of possibilities

EDIT: How to change the inner padding/margin of the TextField

You could play around with the InputDecoration and the decoration property of the TextField. For instance, you could do something like this:

const TextField(
  decoration: InputDecoration(
    contentPadding: EdgeInsets.symmetric(vertical: 40.0),
  ),
)