Just a simple proof-of-concept script showing the basic login / logout process.
Added the register_user() function and fixed a small syntax error.

<?php

/**
 *  Copyright (C) 2009, Suhana
 *  All rights reserved.
 *  
 *  Redistribution and use in source and binary forms, with or without
 *  modification, are permitted provided that the following conditions are met:
 *  1. Redistributions of source code must retain the above copyright
 *     notice, this list of conditions and the following disclaimer.
 *  2. Redistributions in binary form must reproduce the above copyright
 *     notice, this list of conditions and the following disclaimer in the
 *     documentation and/or other materials provided with the distribution.
 *  3. Neither the name of the copyright holder nor the
 *     names of their contributors may be used to endorse or promote products
 *     derived from this software without specific prior written permission.
 *  
 *  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDER ''AS IS'' AND ANY
 *  EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
 *  WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 *  DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE FOR ANY
 *  DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
 *  (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 *  LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
 *  ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 *  (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 *  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

/**
 * Revision History
 *
 * 0.2 Fri 11 Dec 2009
 *     Added register_user(), SQL table definition and fixed a syntax error
 *     in show_last_visit.
 *
 * 0.1 Wed 09 Dec 2009
 *     Initial Revision
 */

/**
 * Table (Users) Definition:
 *  
 *      ID        <INTEGER>
 *      Username  <STRING>
 *      Password  <STRING>
 *      LastVisit <INTEGER>
 *  
 *  Assumptions:
 *  
 *      a) The database connection has already been opened (mysql)
 *      b) Sessions have been started
 *  
 *  Caveats:
 *  
 *      Pretty basic stuff here - You need to provide the relevant login form,
 *      links to logout, and whatever else the site may need.
 *      
 *      **** UNTESTED ****
 */

/**
 * SQL to create the table (You can paste this into a phpMyAdmin SQL window)
 *

    --
    -- Table structure for table `Users`
    --

    CREATE TABLE IF NOT EXISTS `Users`
    (
        `ID`        INT(10) UNSIGNED NOT NULL AUTO_INCREMENT,
        `Username`  VARCHAR(15) NOT NULL,
        `Password`  CHAR(32) NOT NULL,
        `LastVisit` INT(10) UNSIGNED NOT NULL DEFAULT '0',

        PRIMARY KEY          (`ID`),
        UNIQUE  KEY `ByName` (`Username`)
    )
    ENGINE=InnoDB DEFAULT CHARSET=utf8 AUTO_INCREMENT=1 ;

    --
    -- End
    --

 *
 */

/**
 * Returns TRUE if the supplied credentials are valid. Also logs the user in
 * and updates the LastVisit value.
 */
function login( $username, $password )
{
    // cleanup the input

    $username = mysql_real_escape_string($username);
    $password = md5($password);

    // try and find the relevant user

    $sql = "SELECT ID, LastVisit FROM Users WHERE ((Username = '$username') AND (Password = '$password'))";
    $rs  = mysql_query($sql);

    // error check

    if (!$rs)
        die(mysql_error());

    // actually grab the row itself ...

    $row = mysql_fetch_assoc($rs);

    // ... and free the result set

    mysql_free_result($rs);

    // make sure we've actually found somebody

    if (!$row)
        return false;

    // woohoo! now popuplate the session variables ...

    $_SESSION['UserID']    = $row['ID'];
    $_SESSION['LastVisit'] = $row['LastVisit'];

    // ... and update the time this user logged in

    $sql = "UPDATE Users SET LastVisit = " . time() . " WHERE ID = " . $row['ID'];

    // again, quick error check (just in case)

    if (!mysql_query($sql))
        die(mysql_error());

    // and return

    return true;
}

/**
 * Logs the user out of the current session
 */
function logout( )
{
    // just clear the variables

    $_SESSION['UserID']    = 0;
    $_SESSION['LastVisit'] = 0;
}

/**
 * Returns TRUE if the user is currently logged in
 */
function is_logged_in( )
{
    // idiot check

    if (!isset($_SESSION['UserID']))
        return false;

    // okay, but it might be 0 (after a logout ...)

    if ($_SESSION['UserID'] == 0)
        return false;

    // woohoo!

    return true;
}

/**
 * Retrieves the current user id (or 0 if not logged in)
 */
function get_user_id( )
{
    // idiot check

    if (!is_logged_in())
        return 0;

    // return the important bit

    return $_SESSION['UserID'];
}

/**
 * Retrieves the last time the user logged in (or 0 if not/never logged in)
 */
function get_last_visit( )
{
    // idiot check

    if (!is_logged_in())
        return 0;

    // return the important bit

    return $_SESSION['LastVisit'];
}

/**
 * Displays "Last Visit: ...", the last time the user successfully logged in.
 */
function show_last_vist( )
{
    if (!is_logged_in())
        return;

    echo "Last Visit: ";

    $last_vist = get_last_visit();

    if (!$last_vist)
    {
        // oo - we've never logged in before

        echo "Never";
    }
    else
    {
        // format here, rather than at SQL level thus keeping display logic
        // separate from the back-end.

        echo date("Ymd His", $last_visit); 
    }
}

/**
 * Registers a new user account, return TRUE on success, FALSE if the
 * username already exists.
 */
function register_user( $username, $password )
{
    // again, cleanup the variables

    $username = mysql_real_escape_string($username);
    $password = md5($password);

    // and insert the data

    $sql  = "INSERT INTO Users (ID, Username, Password, LastVisit) ";
    $sql .= "VALUES (NULL, '" . $username . "', '" . $password . "', 0)",

    // We use NULL int THE ID field which has the auto-increment attribute
    // to safely generate the next ID #.

    // Notice, we specify exactly what fields are being inserted into (always
    // good practice)

    if (!mysql_query($sql))
    {
        if (mysql_errno() == 1062)
        {
            // oops - looks like the username already exists!

            return false;
        }

        // no idea what went on here ...

        die(mysql_error());
    }

    return true;
}