Open Guild management window from a guild monument. Depending on your role, you will have different abilities available. In this tutorial, a default Viscount role will be used. Authority -> Sacrifice option is usually available for low ranked members and just tries to burn donations previously placed inside monument by higher tier members
Put something valuable inside monument by drug and dropping it to monument window and press "Sacrifice" button
Claim support points value will be increased if items you placed are accepted by the Gods. Guild monument will be automatically checked at midnight and if support points amount is higher than maintenance cost upgrade bar will be filled and slightly moved from a zero point. Claim radius and upgrade bar will be increased constantly if you maintained support points pull regularly and at some day progress bar will be 100% filled.
Keep in mind that maintenance cost will also increase as your claim area grows.