Getting picklist field options in list in apex classs

Display pick list values in your custom page through dyanamic apex .You can check below link it will help  .

https://developer.salesforce.com/blogs/developer-relations/2008/12/using-the-metadata-api-to-retrieve-picklist-values.html

If you want in a string array or list then you can use below code .

public List getPickListValuesIntoList(){
       List pickListValuesList= new List();
  Schema.DescribeFieldResult fieldResult = ObjectApiName.FieldApiName.getDescribe();
  List ple = fieldResult.getPicklistValues();
  for( Schema.PicklistEntry pickListVal : ple){
   pickListValuesList.add(pickListVal.getLabel());
  }     
  return pickListValuesList;
    }