The answer to your first question is yes, anyone can sponsor it.

As for the mechanics...this has been discussed at length, so a search may be in order, but will try to give you a short primer (I'm assuming ECO to BIZ):

Miles: Booking classes Y|B can be upgraded online. For booking classes M|H a MP certificate is required (2 weeks to get, but can be expedited, fee waived for 1Ks). These can be confirmed in advance when I inventory is available on the LH flight.

SWUs: A printed SWU must be ordered from MP (same deal as the mileage cert). This is presented at check-in and the UG is only on a stand-by, space-available basis. Booking classes of V or higher are required.