how do i select from a database and store values in an array with a function?

Currently your getusers() function is incorrect

You could adjust your getusers() function to return an array of your users like so:

function getusers() {
    //db parameters here    
    mysql_connect($dbhost, $dbuser, $dbpass) or die("MySQL Error: " . mysql_error());
    mysql_select_db($dbname) or die("MySQL Error: " . mysql_error());
    $query = "SELECT user_name FROM userinfo";
    $result = mysql_query($query);
    $users = array();
    while ($row = mysql_fetch_array($result, MYSQL_ASSOC)) {
        $users[] = $row['user_name'];
    }
    mysql_Close($conn);
    return $users;
}

And then in another file, you can include this:

include('usernames.php');
$users  = getusers();

foreach($users as $user) {
    getTax($user);
}

function getTax($user) {
    // do something with $user here
    echo $user; // prints the username
}

First I feel compelled to say that you should be using PDO, especially since PDOStatement::fetchAll does most of what you want. This tutorial looks relatively decent.

Here's a bit of a re-write, but it will do everything you want it to:

// let yourself cache the connection. That will save you processing time
function getusers( $connection, $dbname = DB_NAME )
{
    if( !$connection ) 
    {
        return FALSE; // we can't do anything here.
    }
    // Selecting a db inside of a function can cause problems for others using
    // your code (if you use $connection as a parameter). Instead explicitly 
    // use the database
    $query  = "SELECT user_name FROM `$dbname`.`userinfo`";
    // you may want to make this cause a return of something other than FALSE, 
    // but you definitely want a way to have some form of early escape here.
    $result = mysql_query($query, $connection) or return FALSE;
    $final = array();
    while($row = mysql_fetch_array($result, MYSQL_ASSOC))
    {
       // append the current user_name to the $final array
       $final[] = $row['user_name'];
    } 
    // you'll need to close the connection elsewhere.
    return $final;
}

In the second file:

include('usernames.php');
$conn  = mysql_connect($dbhost, $dbuser, $dbpass);
$users = getusers( $conn, $dbname ) or die( "MySQL Error: " . mysql_error() );
// foreach... as... will loop through your array automatically.
foreach( $users as $user )
{
    // $user refers to each user_name fetched in getusers
    getTax( $user, $connection, $dbname );
}

// and here is where the cost saving of caching your connection is found:
function getTax( $user, $connection, $dbname = DB_NAME )
{
    if( !$connection ) 
    {
        return FALSE; // we can't do anything here.
    }
    $result = mysql_query( "SELECT * FROM TAX_TABLE WHERE USER_NAME = '$user'", 
                           $connection ) or return FALSE;
    // continue as normal
}