A button itself can be made either with an input tag (type="submit") or with the button tag.
In the former case, your input tag looks something like this:
<input type="submit" value="Login" />
which would create a submit button that reads "Login". Alternatively, then, you could make a button with
<button type="submit">Login</button>
enclosing in the opening and closing tags whatever you want to be displayed on the button. In this latter case, that includes things such as images that you cannot display with a button from an input tag, e.g.
<button type="submit"><img src="padlock.png" alt="" /> Login</button>
Your button should be enclosed in a form that contains the address of the page to send the user to when they click the submit button in it, e.g.
<form action="process_login.php" method="post">
<p>username: <input name="username" type="text" value="" /><br />
password: <input name="password" type="password" value="" /></p>
<p><button type="submit">Login</button></p>
</form>
where, on clicking "login", the user is brought to the process_login.php page, and the data that was entered into the username and password fields becomes available for use by the programming in that page.
To actually program a log on system, you would need to learn some sever-side programming language... You'd need to manage a database, too. I strongly suggest you read up on PHP and MySQL. There are a lot of online guides about picking up the PHP language, and if you get stuck, you could always ask for help on the server-side programming forum (http://http://www.htmlforums.com/f-server-side-programming-19.html/).
If you're not really looking to learn a lot about web development to get an interactive blog, you may want to google for some existing blogging services.