You use the $expand query option.
For example, you have two lists: ListA and ListB. ListA has two fields: Field1 and Field2. ListB has three fields: FieldA, FieldB and LookupField. LookupField looks up to ListA. REST query should be as such:
/_api/web/lists/GetByTitle('ListB')/items?$select=FieldA,FieldB,LookupField/Field1,LookupField/Field2&$expand=LookupField
You select the fields from the list by adding their internal name to the $select query option, and you select fields from the lookup list by using the format LookupField/FieldFromLookupList, and then you add the lookup field to the $expand query option.