How to do create a form ui component select box with a source to fill select box

You can add like this

<field name="formats">
    <argument name="data" xsi:type="array">
        <item name="options" xsi:type="object">Magento\Catalog\Model\Product\AttributeSet\Options</item>
        <item name="config" xsi:type="array">
            <item name="dataType" xsi:type="string">text</item>
            <item name="label" xsi:type="string" translate="true">Formats</item>
            <item name="formElement" xsi:type="string">select</item>
            <item name="source" xsi:type="string">modulename</item>
            <item name="dataScope" xsi:type="string">formats</item>
            <item name="default" xsi:type="string">0</item>
            <item name="validation" xsi:type="array">
                <item name="required-entry" xsi:type="boolean">true</item>
            </item>
        </item>
    </argument>
</field>

This is an approach that is more common at least as of Magento 2.3:

<field name="image_overlay_art" sortOrder="40" formElement="select">
    <settings>
        <dataType>int</dataType>
        <label translate="true">Show Art on Image Overlay</label>
    </settings>
    <formElements>
        <select>
            <settings>
                <options class="\Magento\Config\Model\Config\Source\Yesno"/>
            </settings>
        </select>
    </formElements>
</field>