[SalesForce] How to use Custom Labels in Custom Button or Link

EDIT This is now possible! You can instantiate a dynamic visualforce component in Apex to get this.

public String getLabel(String myLabel ){
    Component.Apex.OutputText output = new Component.Apex.OutputText();
    output.expressions.value = '{!$Label.'+ myLabel + '}';
    return String.valueOf(output.value);
}

ORIGINAL ANSWER

No, you can't reference labels dynamically in apex. You can vote for this idea here. However, you can reference them dynamically from visualforce so you can put them on the page like so:

public class MyController
{
    public String mylabel{get; set;}

    public MyController()
    {
         mylabel='labelname';   
    }
}

<apex:page Controller="MyController">
    <apex:outputText> {!$Label[mylabel]} </apex:outputText>
</apex:page>

Assuming that you need to translate your picklist values the way you translate any other custom label, this is what you should do.

Setup -> Translation settings Enable translation in your org.

Setup -> Translate Select language, "Picklist value" in setup component and your choice of object. The result will display all the picklist fields that is present in the selected object.

Expand the picklist of your choice and write the translated value in 'Picklist value Label Translation' column. Example, if picklist value is 'Earth', then the translated value will be 'Tierra' if the language that is selected in Spanish.

Now if you refresh you VF page, the picklist values will be translated.

*Don't forget to change your language from personal information.