The visa always has to be applied for by the person who intends to travel to Germany. Details on the documents to be presented at the time of application are often available on the webpage of the competent German mission or directly from the mission itself.
For private visits, an invitation is usually required to confirm the purpose of the journey. In case the visitor is not able to fully cover the expenses associated with the trip a formal pledge to cover all costs (declaration of commitment) has to be presented with the visa application. In this case the host can sign the relevant form ("Verpflichtungserklärung") at his/her residency's local authorities (usually Ordnungsamt or Ausländerbehörde).
German missions abroad: Countries A to Z