Year, Month and Day are all public query variables, all you need to do is create a search form with appropriately named inputs.
<form method="get" action="<?php echo home_url( "https://wordpress.stackexchange.com/" ); ?>">
<select name="day">
<?php foreach( range(1,31) as $day_of_month ) : ?>
<option><?php echo $day_of_month; ?></option>
<?php endforeach; ?>
</select>
<select name="monthnum">
<?php foreach( range(1,12) as $month_of_year ) : ?>
<option><?php echo $month_of_year; ?></option>
<?php endforeach; ?>
</select>
<select name="year">
<?php foreach( range(2000,2011) as $_year ) : ?>
<option><?php echo $_year; ?></option>
<?php endforeach; ?>
</select>
<input type="submit" id="searchsubmit" value="Search" />
</form>
Totally untested, but it should do the trick, let me know of any problems.