How do I use an if/else statement to determine if a field is filled in?
You can use the length Twig filter for that.

{% if entry.featureImage | length %}
    {% set image = entry.featureImage.first() %}
    &lt;div class="imagewrapper"&gt;
       &lt;img src="{{ image.getUrl() }}" width="{{ image.getWidth('banner') }}" height="{{ image.getHeight('banner') }}"&gt;
    &lt;/div&gt;
{% endif %}


If there isn't an image in featureImage then nothing will be output.