How to display HTML <FORM> as inline element?

Move your form tag just outside the paragraph and set margins / padding to zero:

<form style="margin: 0; padding: 0;">
  <p>
    Read this sentence 
    <input style="display: inline;" type="submit" value="or push this button" />
  </p>
</form>

<form> cannot go inside <p>, no. The browser is going to abruptly close your <p> element when it hits the opening <form> tag as it tries to handle what it thinks is an unclosed paragraph element:

<p>Read this sentence 
 </p><form style='display:inline;'>

According to HTML spec both <form> and <p> are block elements and you cannot nest them. Maybe replacing the <p> with <span> would work for you?

EDIT: Sorry. I was to quick in my wording. The <p> element doesn't allow any block content within - as specified by HTML spec for paragraphs.

You can try this code:

<form action="#" method="get" id="login" style=" display:inline!important;">

  <label for='User'>User:</label> 
  <input type='text' name='User' id='User'>

  <label for='password'>Password:</label><input type='password' name='password' id='password'>
  <input type="submit" name="log" id="log" class="botton" value="Login" />

</form> 

The important thing to note is the css style property in the <form> tag.

display:inline!important;