How do I make display a specific post based on what the day of the week it is? I can do it in PHP, but I'm having trouble converting it to twig. 

Here's the PHP:

$day = date("l");
date_default_timezone_set('America/Chicago');



if ($day == "Saturday")
{
    echo "&lt;p&gt;&lt;b&gt;SATURDAY SPECIALS&lt;/b&gt;&lt;/p&gt;";
    echo "&lt;/div&gt;&lt;div class=\"mod1\"&gt;";
    echo "&lt;p&gt;FOOD&lt;/p&gt;";
    echo "&lt;h3&gt;Half priced desserts&lt;/h3&gt;";
    echo "&lt;p&gt;DRINK&lt;/p&gt;";
    echo "&lt;h3&gt;$1 off Seasonal Pints&lt;/h3&gt;";

}
elseif ($day == "Sunday")
{
    echo "&lt;p&gt;&lt;b&gt;GAMEDAY SPECIALS&lt;/b&gt;&lt;/p&gt;";
    echo "&lt;/div&gt;&lt;div class=\"mod1\"&gt;";
    echo "&lt;p&gt;FOOD&lt;/p&gt;";
    echo "&lt;h3&gt;One Free Kids Meal w/ each Adult Meal&lt;/h3&gt;";
    echo "&lt;p&gt;DRINK&lt;/p&gt;";
    echo "&lt;h3&gt;$3 on ALL Bottled Beers&lt;/h3&gt;";    }
elseif ($day == "Monday")
{
    echo "&lt;p&gt;&lt;b&gt;MONDAY SPECIALS&lt;/b&gt;&lt;/p&gt;";
    echo "&lt;/div&gt;&lt;div class=\"mod1\"&gt;";
    echo "&lt;p&gt;FOOD&lt;/p&gt;";
    echo "&lt;h3&gt;$1 Tenders &lt;br /&gt;(5 piece min.)&lt;/h3&gt;";
    echo "&lt;p&gt;DRINK&lt;/p&gt;";
    echo "&lt;h3&gt;$2 Lonestar Pints&lt;/h3&gt;";  }
elseif ($day == "Tuesday")
{
    echo "&lt;p&gt;&lt;b&gt;TUESDAY SPECIALS&lt;/b&gt;&lt;/p&gt;";
    echo "&lt;/div&gt;&lt;div class=\"mod1\"&gt;";
    echo "&lt;p&gt;FOOD&lt;/p&gt;";
    echo "&lt;h3&gt;$.50 Boneless Wings &lt;br /&gt; (10 piece min.)&lt;/h3&gt;";
    echo "&lt;p&gt;DRINK&lt;/p&gt;";
    echo "&lt;h3&gt;$4 Margaritas&lt;/h3&gt;";  }
elseif ($day == "Wednesday")
{
    echo "&lt;p&gt;&lt;b&gt;WEDNESDAY SPECIALS&lt;/b&gt;&lt;/p&gt;";
    echo "&lt;/div&gt;&lt;div class=\"mod1\"&gt;";
    echo "&lt;p&gt;FOOD&lt;/p&gt;";
    echo "&lt;h3&gt;Half price APPs!&lt;/h3&gt;";
    echo "&lt;p&gt;DRINK&lt;/p&gt;";
    echo "&lt;h3&gt;$3 shots of Jameson &amp; Jager&lt;/h3&gt;";
}
elseif ($day == "Thursday")
{
    echo "&lt;p&gt;&lt;b&gt;THURSDAY SPECIALS&lt;/b&gt;&lt;/p&gt;";
    echo "&lt;/div&gt;&lt;div class=\"mod1\"&gt;";
    echo "&lt;p&gt;FOOD&lt;/p&gt;";
    echo "&lt;h3&gt;2 for $10 Wingzup Burgers&lt;/h3&gt;";
    echo "&lt;p&gt;DRINK&lt;/p&gt;";
    echo "&lt;h3&gt;$3 Draft Beers all day&lt;/h3&gt;";
}
else
{
    echo "&lt;p&gt;&lt;b&gt;FRIDAY SPECIALS&lt;/b&gt;&lt;/p&gt;";
    echo "&lt;/div&gt;&lt;div class=\"mod1\"&gt;";
    echo "&lt;p&gt;FOOD&lt;/p&gt;";
    echo "&lt;h3&gt;$2 Chili Pies&lt;/h3&gt;";
    echo "&lt;p&gt;DRINK&lt;/p&gt;";
    echo "&lt;h3&gt;$10 Pitchers (Bud Lt./Ziegenbock/Lone Star)&lt;/h3&gt;";
}
To get the current date and time in Twig use the string "now" and filter it with the date() filter to return it in the format you need (see the list for supported parameters).

Then do the if / elseif conditionals similar to how you'd do it in PHP. Another option would be to use the Craft specific switch tag.

{% switch "now" | date("l") %}

    {% case "Monday" %}
        {# Do Monday stuff #}

    {% case "Tuesday" %}
        {# Do Tuesday stuff #}

    {% case "Wednesday" %}
        {# Do Wednesday stuff #}

    {# etc. #}

{% endswitch %}