$sql = "select * from table_name where date >= DATE_SUB(NOW(), INTERVAL 1 DAY)";

Here is your select menu:

<select name="selected_interval">
<option value="0 DAY">Today</option>
<option value="1 DAY">Yesterday</option>
<option value="1 MONTH">Last month</option>
<option value="30 YEAR">All time</option>
</select>

Than your query will be:

$sql = "select * from table_name where date >= DATE_SUB(NOW(), INTERVAL ".$_POST['selected_interval'].")";

I did not tested this code, but I think this is a good start point.

$result = mysql_query('SELECT * FROM `table_name` WHERE 'date' >= $from_date AND 'date' <= $to_date ORDER BY `date` DESC');

so i just have to pass values of variables $to_date and $from _date.
but getting error, so just help me with these code.

With this:
$result = mysql_query("SELECT * FROM table_name WHERE date >= " . $from_date . " AND date <= " . $to_date . " ORDER BY date DESC");

I think your problems arise from your interchanging of ' and `. You can avoid those errors by concatenating strings as I did in the revised SQL statement.