I believe the pre-merger process is still in place. Lufthansa didn't switch over to SHARES. However, there has been talk and speculation about the roll-out of an electronic GPU process, although the terms and process are unknown until it becomes available.
The two main methods are (a) get a GPU printed for use on V fares or higher (not S, T, L, K, or W), and (b) use miles for a Star Alliance upgrade. Method (a) requires a GPU from a 1K or Global Services account, and the GPU must have an expiration date that is after your planned date of travel. Method (b) requires an eligible fare, which are the most expensive ones -- Y and B. For more information, please see the United Star Alliance Upgrades page --
http://www.united.com/web/en-US/cont...rade/saua.aspx
Another option is to look for an inexpensive Business fare. While these may be less expensive than Y or B fares, they are often very restricted with regard to changes and cancellations, and often they must be booked at least two months in advance.
Good luck!